Discussion:
Abstract Algebra Broken
Peter
2020-10-17 16:18:27 UTC
We are not in algebra per se. We are in the curriculum of
abstract algebra. I have no idea how you could come to
disagree with this language particularly when you find no
actual fault with the language. I have linked to numerous
online references here; not as numerous as Lalo though. It is
almost as if you want to deny that the real numbers do fit
the ring definition.
Consider the following. Let
a_0, a_1, a_2, ... b_0, b_1, b_2, ...
be (not necessarily distinct) sequences of real numbers subject
to the requirements that only finitely many members are
non-zero.
Define the _sum_ of them to be
(a_1 + b_1), (a_2 + b_2, (a_3 + b_3), ...
And the _product_ of them to be
sum_{k=0}^infty sum_{n=0}^k a_n b_{k-n}.
I claim that the set of such sequences under sum and addition
as defined is a ring. Do you agree?
Yes or no?
No, but the problem is larger than a yes/no answer. I say yes, I see
how the polynomial products and sums work out to another polynomial;
but I say no because those sums which build the polynomial are built
via the ring operator, and the products in the terms of the
polynomial are built with that ring product, and they do not fit the
ring definition. This is not a yes/no situation. The ring of
polynomials with real coefficients is not ring behaved.
That ring is, but for notation, the same as the ring of
polynomials of one indeterminate over the real numbers denote
R[X] where R is the real numbers. The element
a_0 + a_1 X + a_2 X^2 +...
of R[X] corresponds to
a_0, a_1, a_2, ...
Do you understand that?
I understand the product and sum of polynomials and I see that at
the outer level the ring behavior is upheld but it is this method
of dismantling the polynomial which yields the conflict. Each
polynomial is a sum of terms and those terms clearly must obey the
ring definition too. Each term contains products and those products
must obey the ring definition. Otherwise there is a conflict. The
conflict is best exposed on the polynomial with real coefficients
and so to specify an instance
a1 X and witness that this product is not ring behaved;
I've asked you twice before what "ring behaved" means. Would you
like to say now? If you wish, answer with respect to a1 X rather
than generally (though generally would be best).
And yet you don't.
. But Peter if all
that we do is cover the same ground again that will not be
meaningful. You have had a chance. If all that you mean to do is
repeat the same defense then why bother? This is a big deal, so it is
worth trying again. But it is relevant to take a variation from the
prior course. In fact I am happy to expound for I think I did  bump
into the reason that I use this terminology. The Ring definition is
not a concrete thing. Whereas in the definition of real numbers we
can actually name a real number 1.23 and I can comfortably say 'is
real' the ring definition really only defines requirements for
operators, and those operators perform actions. They have behavior.
They take two elements and yield one element.  But furthermore there
is nothing concrete about them. Even the real value I would say is
ring behaved. To say that the real number 'is a ring' has poor
grammatical value.
Bugger its 'grammatical value', it's downright false to say that the
real number 'is a ring'.  A ring is three things (S,+,*) where S is a
set and + and * are both binary operations defined on that set.  Those
operations are required to satisfy certain conditions (such as
associativity) that you can look up.  An example is S being the set of
real numbers and + and * being the usual arithmetical operations.  To
wrote of one element of S as being a ring is silly
write of one

Sorry
To say that the real number is ring behaved is
much more natural. Both I believe mean to obey the rules of the ring
definition
The definition of a ring refers to a triple, above written as (S,+,*).
It is silly to write of an element of S as obeying the rules of the ring
definition.  Here's an analogy: London is defined to be the capital of
the UK (yes, I know there are other Londons but for my purposes it's
London as defined by me that I'm writing about.)  Does John Smith who
lives on Eaton Square (a place in London) obey the rules of the
definition of London?  No.  Is that a problem?  No.
You mention 1.23 X.  In terms of the 'sequences of real numbers subject
to the requirements that only finitely many members are non-zero'
definition of polynomial, that is 0, 1.23, 0, 0, ....  It is also the
product of 1.23, 0, 0, 0, ... and 0, 1, 0, 0, ...  (Which is no more
remarkable than six being both 6 and the product of 2 and 3.)
, but the definition does not describe a set of elements;
it describes what a set of elements can do. It defines their
behavior.
that this term is in sum with other terms that will not obey the
ring definition; and of course we need just one such polynomial
to fail in order to have a falsification; one black swan proves
that not all swans are white and so we can go a bit further with
our specificity of that black swan 1.23 X which does not obey the
ring definition. This is as concrete an instance as I can muster
without breaking any of AA's rules. So there you have it: a ring
behaved polynomial that is not ring behaved. It is nice of you to
make another attempt here. For a while you were the only one who
could face the black swan. Others here have devolved into
statements like That product is not a product The sum is not a
sum Whereas the X is nearly nothing at all Were operators only
just defined in this subject Peter? The ring definition comes
some pages before the introduction of the polynomial in AA right?
Should a subject which cares to define operators use them more
carefully? Do elements contain operators? If they do then those
operators ought to resolve right? This is exactly what the AA
I don't know what 'resolve' means in this context.  Nor am I sure I know
what you mean by elements containing operators.  Are you taking about
the way something might be written?  E.g., here's an element of the ring
of integers: 6, and it equals 2*3, and '2*3' contains the symbol '*'. To
say, instead, '6 contains *' would be potty.
polynomial does not do.
only just defined in this subject Peter? The ring definition comes
some pages before the introduction of the polynomial in AA right?
Should a subject which cares to define operators use them more
carefully? Do elements contain operators? If they do then those
operators ought to resolve right? This is exactly what the AA
polynomial does not do. Now you are dodging the black swan; something
that you used to be unafraid of. I have already conceded to you that
products of polynomials yield polynomials and sums of polynomials
yield polynomials, but my argument is on the contents of those
polynomials. I dismantle the polynomial to expose the conflict.
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
Lalo T.
2020-10-17 21:31:08 UTC
< There is no fog present in the polysign numbers

I am not saying 'Polysign numbers are fuzzy/hazy'

Maybe I didn choose the right words, or express it in an unclear way.

I am contending that the ALGEBRA behind Polysign Numbers p2 and the ALGEBRA
behind Real Numbers is different (also for the rest of the
'polysigned Pn numbers' with n>2, where their ALGEBRA, compared with the ALGEBRA
of some other number systems, like quaternions, complex numbers,icosians is
different (in the compartimentalized VS non-compartimentalized versions of algebra)

" The sign function or signum function """extracts""" the sign of a real number,
by mapping the set of real numbers to the set of the three reals {-1,0,1}. It can
be defined as follows :

sgn : ℝ -> {x ∈ ℝ : |x| = 1} ⋃ {0}

x ↦ sgn(x) =

-1 if x < 0
0 if x = 0
1 if x > 0 "
in https://en.wikipedia.org/wiki/Sign_(mathematics)#Real_sign_function
(it can be other definition of sgn(..) )

well, you can define the sgn(..) with output into whatever you want, maybe with
output like the words "negative", "positive"
(inside/outside the original set? or, what is my reference set ?)

In any case, what is the meaning of """extracts""" in the above text ?
or why necesarilly put in the same context sgn(..) with Absolute Value function?
Is this the case in polysigned numbers ?

That is an inkling of why "sign" in ℝ, and the "sign" of Polysign are different.

I think I can judge the 'compartimentalized algebra' (that one may potentially
extrapolate from polysigns) from the conventional algebra perspective, but, just
in the same fashion that certain tongue/language judges another tongue/language.

Different tongues maybe are pointing to the same thing, but that does not change
the fact that they are two different "maps". (referring to algebra)

The polysigned numbers Pn with n as any integer, will not classify as
conventional "algebraic structures", rather, compartimentalized algebraic
structures.

In this specific context, I think will be a mistake to mix concepts of these two
different algebras, or try to impose one over the other, as much "nearby" as
these two languages may be. But, by default, one has ingrained one language,
in how one build sentences, unless, one have certain domain in another language.
"I can not go, everywhere, presupposing that every person that I encounter will
speak english, if I only know english" (in the algebra context)

"...the set of natural numbers is not closed under taking additive inverses. "

One can not say, in your system, that the magnitude-component (length component)
have additive inverse, rather one says that the term ( this is, the combination
of the index-ray-component("direction") with the length-component(magnitude )
have additive inverse, not necessarily using a "reverse sign unary operator"
(whatever that means in a polysign context )

< How many tongues are there here:

just one extra language/tongue, in the sense that some polysigned number Pn with
some specific n, for example n=5 could be classified as an algebraic structure,
just, I am not convinced that can be classified in conventional structures,
like a ring, field, ...etc, although undoubtedly, has some resemblance.

Maybe, another story would be, if some other abstract area of maths if used,
but Algebra (or at least a portion of it) evolved as a "non-compartimentalized"
branch, if you want.

(negative element) VS (negative, element)

The author Alberto Martínez, in his elegant treatise "Negative numbers"
https://www.amazon.com/Negative-Math-Mathematical-Rules-Positively/dp/0691133913

wrote masterfully :

" Yet this pursuit is rarely carried out nowadays. Scarcely anyone designs new
maths as methods of representation. Virtually nobody imputes to traditional
algebraic methods any blame for instances where the symbolism generates
unsatisfactory or bizarre results. Instead, when equations seem to lack
meaning, or seem to signify things quite unintelligible, especially in
modern physics, we often hear the following attitudes. Some teachers tell
students that the problem just cannot be understood in terms of common
sense. Some say that language, ordinary words, are not appropriate
for describing the underlying physical relations. They sometimes
also say that diagrams cannot exactly describe the physical system.
Some also say that usual notions of cause and effect are just
inadequate for understanding certain microphysical processes.
However, virtually nobody says that maybe it is the algebra that is defective. "
(brief excerpts in connection with reviews or scholarly analysis)
Tim Golden BandTech.com
2020-10-18 13:50:26 UTC
Post by Lalo T.
< There is no fog present in the polysign numbers
I am not saying 'Polysign numbers are fuzzy/hazy'
Maybe I didn choose the right words, or express it in an unclear way.
I am contending that the ALGEBRA behind Polysign Numbers p2 and the ALGEBRA
behind Real Numbers is different (also for the rest of the
I have to interrupt you right here and say that no; P2 are the real numbers. There is no distinction that can be made between them. That P2 are a simplex coordinate system thanks to their rule:
- 1 + 1 = 0
has been known by different methods, but the result is the same. That P2 are rotationally behaved is true though possibly not uttered before. That P2 are not as fundamental as has been preached in the academic institutions; now this is something new, but the algebra of the real number and of P2 are one and the same. It is an interesting awareness to attempt a distinction, but that you claim there is one ought to be substantiated. By the time you get to signum() or distance() I'm pretty sure you won't have any problems. As to which is greater: -1 or +1 I could see an argument for -1 being far greater in that it can generate +1, but that is a quip. Well maybe there is something here.
Post by Lalo T.
'polysigned Pn numbers' with n>2, where their ALGEBRA, compared with the ALGEBRA
of some other number systems, like quaternions, complex numbers,icosians is
different (in the compartimentalized VS non-compartimentalized versions of algebra)
" The sign function or signum function """extracts""" the sign of a real number,
by mapping the set of real numbers to the set of the three reals {-1,0,1}. It can
sgn : ℝ -> {x ∈ ℝ : |x| = 1} ⋃ {0}
x ↦ sgn(x) =
-1 if x < 0
0 if x = 0
1 if x > 0 "
in https://en.wikipedia.org/wiki/Sign_(mathematics)#Real_sign_function
(it can be other definition of sgn(..) )
well, you can define the sgn(..) with output into whatever you want, maybe with
output like the words "negative", "positive"
(inside/outside the original set? or, what is my reference set ?)
In any case, what is the meaning of """extracts""" in the above text ?
or why necesarilly put in the same context sgn(..) with Absolute Value function?
Is this the case in polysigned numbers ?
That is an inkling of why "sign" in ℝ, and the "sign" of Polysign are different.
Well I'd be more concerned with these functions in Pn, where distance() will hold up, but signum() is not going to. We have general dimensional values. They are built from the form
s x
where s is sign and x is magnitude and clearly this fundamental form allows
signum( sx ) === s
but general values aren't going to support this. There is almost support for an antisignum() because the balance of the terms allows for the reduction of one component to always be zero; though there could also be more than one zero term. This has a subtle consequence of saving data so that polysign can claim a more compact representation than cartesian high dimensional values: The sign bit of the cartesian form is gone in polysign, and the zero component can be specified in far less bits than it takes to make the cartesian form. So for instance a 32 dimensional value saves 32-5 bits in polysign versus cartesian. That said, the savings is paltry if we are using high resolution data. Still, it is there.
Post by Lalo T.
I think I can judge the 'compartimentalized algebra' (that one may potentially
extrapolate from polysigns) from the conventional algebra perspective, but, just
in the same fashion that certain tongue/language judges another tongue/language.
Different tongues maybe are pointing to the same thing, but that does not change
the fact that they are two different "maps". (referring to algebra)
The polysigned numbers Pn with n as any integer, will not classify as
conventional "algebraic structures", rather, compartimentalized algebraic
structures.
But again they do. The sum and product are well defined and well behaved. Really in this way we could argue that polysign themselves are a stepping stone. What you are describing might be the next stepping stone, but polysign are very well connected to tradition. All that is required to recover them is a willingness to generalize sign. We can speak of z in Pn, and we have
z1( z2 @ z3 ) = z1 z2 @ z1 z3
z1 z2 = z2 z1
and so forth and in any dimension.
Post by Lalo T.
In this specific context, I think will be a mistake to mix concepts of these two
different algebras, or try to impose one over the other, as much "nearby" as
these two languages may be. But, by default, one has ingrained one language,
in how one build sentences, unless, one have certain domain in another language.
"I can not go, everywhere, presupposing that every person that I encounter will
speak english, if I only know english" (in the algebra context)
"...the set of natural numbers is not closed under taking additive inverses. "
One can not say, in your system, that the magnitude-component (length component)
have additive inverse, rather one says that the term ( this is, the combination
of the index-ray-component("direction") with the length-component(magnitude )
have additive inverse, not necessarily using a "reverse sign unary operator"
(whatever that means in a polysign context )
Well in P4 the additive inverse of
- 1 + 2 * 4
is
- 3 + 2 # 4
so clearly the additive inverse does not have the extreme shorthand wave of flipping signs but pretty clearly the sum of these quantities is
- 4 + 4 * 4 # 4
which is balanced. And sure enough if you step around in such a pattern you will land right back where you started. That the geometry is tightly tied into the algebra is really one of the most remarkable points; and of course that it is a nonorthogonal geometry; that the simplex geometry is natural; this is exceptionally excellent. That this exists yet has gone overlooked by existing math suggests a next stone. Possibly that next stone will be more as you see polysign, but from what I see first polysign will have to be absorbed. We are merely Shakespear's monkeys with filters. Polysign proves it. The filters that have been enforced were wrong. Real analysis as a branch was probably developed off of the resistance to the negative value. The preaching of the reals as fundamental was merely a new religiosity in the face of an older religiosity. Strangely though the denial of the existence of negative values and the need to call the two-signed form 'real' is a fight not worth having. When done correctly
s x
shows the unsigned value has a more fundamental status. There never was any fight to begin with. Getting general dimensional is much more interesting and not even Descartes would argue that he could conjure up a Euclidean plane from two real valued lines. The plane was already there on the paper before him. He used a baseline often enough and probably habitually. But there is no usage of an origin in his work that I have seen. Even after his disciples developed an addressable plane there is no claim other than representation of that plane by two values. Polysign however demand their geometry and after the P2 line comes the P3 plane. Meanwhile AA people are busily requiring infinite dimensional systems to recover the complex plane. May the farce be with you!
Post by Lalo T.
just one extra language/tongue, in the sense that some polysigned number Pn with
some specific n, for example n=5 could be classified as an algebraic structure,
just, I am not convinced that can be classified in conventional structures,
like a ring, field, ...etc, although undoubtedly, has some resemblance.
Maybe, another story would be, if some other abstract area of maths if used,
but Algebra (or at least a portion of it) evolved as a "non-compartimentalized"
branch, if you want.
(negative element) VS (negative, element)
The author Alberto Martínez, in his elegant treatise "Negative numbers"
https://www.amazon.com/Negative-Math-Mathematical-Rules-Positively/dp/0691133913
" Yet this pursuit is rarely carried out nowadays. Scarcely anyone designs new
maths as methods of representation. Virtually nobody imputes to traditional
algebraic methods any blame for instances where the symbolism generates
unsatisfactory or bizarre results. Instead, when equations seem to lack
meaning, or seem to signify things quite unintelligible, especially in
modern physics, we often hear the following attitudes. Some teachers tell
students that the problem just cannot be understood in terms of common
sense. Some say that language, ordinary words, are not appropriate
for describing the underlying physical relations. They sometimes
also say that diagrams cannot exactly describe the physical system.
Some also say that usual notions of cause and effect are just
inadequate for understanding certain microphysical processes.
However, virtually nobody says that maybe it is the algebra that is defective. "
(brief excerpts in connection with reviews or scholarly analysis)
Tim Golden BandTech.com
2020-10-18 14:06:43 UTC
Post by Lalo T.
The author Alberto Martínez, in his elegant treatise "Negative numbers"
https://www.amazon.com/Negative-Math-Mathematical-Rules-Positively/dp/0691133913
" Yet this pursuit is rarely carried out nowadays. Scarcely anyone designs new
maths as methods of representation. Virtually nobody imputes to traditional
algebraic methods any blame for instances where the symbolism generates
unsatisfactory or bizarre results. Instead, when equations seem to lack
meaning, or seem to signify things quite unintelligible, especially in
modern physics, we often hear the following attitudes. Some teachers tell
students that the problem just cannot be understood in terms of common
sense. Some say that language, ordinary words, are not appropriate
for describing the underlying physical relations. They sometimes
also say that diagrams cannot exactly describe the physical system.
Some also say that usual notions of cause and effect are just
inadequate for understanding certain microphysical processes.
However, virtually nobody says that maybe it is the algebra that is defective. "
(brief excerpts in connection with reviews or scholarly analysis)
Iconic Arithmetic

The Design of Mathematics for human Understanding

William Bricken, Ph.D.

https://archive.org/stream/iconicarithmetic01will/iconicarithmetic01will_djvu.txt

quotes Martinez which is how I found him. Very apt. A whole can of worms: http://iconicmath.com/algebra/james/
Tim Golden BandTech.com
2020-10-18 13:51:15 UTC
Post by Lalo T.
< There is no fog present in the polysign numbers
I am not saying 'Polysign numbers are fuzzy/hazy'
Maybe I didn choose the right words, or express it in an unclear way.
I am contending that the ALGEBRA behind Polysign Numbers p2 and the ALGEBRA
behind Real Numbers is different (also for the rest of the
'polysigned Pn numbers' with n>2, where their ALGEBRA, compared with the ALGEBRA
of some other number systems, like quaternions, complex numbers,icosians is
different (in the compartimentalized VS non-compartimentalized versions of algebra)
" The sign function or signum function """extracts""" the sign of a real number,
by mapping the set of real numbers to the set of the three reals {-1,0,1}. It can
sgn : ℝ -> {x ∈ ℝ : |x| = 1} ⋃ {0}
x ↦ sgn(x) =
-1 if x < 0
0 if x = 0
1 if x > 0 "
in https://en.wikipedia.org/wiki/Sign_(mathematics)#Real_sign_function
(it can be other definition of sgn(..) )
well, you can define the sgn(..) with output into whatever you want, maybe with
output like the words "negative", "positive"
(inside/outside the original set? or, what is my reference set ?)
In any case, what is the meaning of """extracts""" in the above text ?
or why necesarilly put in the same context sgn(..) with Absolute Value function?
Is this the case in polysigned numbers ?
That is an inkling of why "sign" in ℝ, and the "sign" of Polysign are different.
I think I can judge the 'compartimentalized algebra' (that one may potentially
extrapolate from polysigns) from the conventional algebra perspective, but, just
in the same fashion that certain tongue/language judges another tongue/language.
Different tongues maybe are pointing to the same thing, but that does not change
the fact that they are two different "maps". (referring to algebra)
The polysigned numbers Pn with n as any integer, will not classify as
conventional "algebraic structures", rather, compartimentalized algebraic
structures.
In this specific context, I think will be a mistake to mix concepts of these two
different algebras, or try to impose one over the other, as much "nearby" as
these two languages may be. But, by default, one has ingrained one language,
in how one build sentences, unless, one have certain domain in another language.
"I can not go, everywhere, presupposing that every person that I encounter will
speak english, if I only know english" (in the algebra context)
"...the set of natural numbers is not closed under taking additive inverses. "
One can not say, in your system, that the magnitude-component (length component)
have additive inverse, rather one says that the term ( this is, the combination
of the index-ray-component("direction") with the length-component(magnitude )
have additive inverse, not necessarily using a "reverse sign unary operator"
(whatever that means in a polysign context )
just one extra language/tongue, in the sense that some polysigned number Pn with
some specific n, for example n=5 could be classified as an algebraic structure,
just, I am not convinced that can be classified in conventional structures,
like a ring, field, ...etc, although undoubtedly, has some resemblance.
Maybe, another story would be, if some other abstract area of maths if used,
but Algebra (or at least a portion of it) evolved as a "non-compartimentalized"
branch, if you want.
(negative element) VS (negative, element)
The author Alberto Martínez, in his elegant treatise "Negative numbers"
https://www.amazon.com/Negative-Math-Mathematical-Rules-Positively/dp/0691133913
" Yet this pursuit is rarely carried out nowadays. Scarcely anyone designs new
maths as methods of representation. Virtually nobody imputes to traditional
algebraic methods any blame for instances where the symbolism generates
unsatisfactory or bizarre results. Instead, when equations seem to lack
meaning, or seem to signify things quite unintelligible, especially in
modern physics, we often hear the following attitudes. Some teachers tell
students that the problem just cannot be understood in terms of common
sense. Some say that language, ordinary words, are not appropriate
for describing the underlying physical relations. They sometimes
also say that diagrams cannot exactly describe the physical system.
Some also say that usual notions of cause and effect are just
inadequate for understanding certain microphysical processes.
However, virtually nobody says that maybe it is the algebra that is defective. "
(brief excerpts in connection with reviews or scholarly analysis)
Tim Golden BandTech.com
2020-10-18 12:27:54 UTC
We are not in algebra per se. We are in the curriculum of
abstract algebra. I have no idea how you could come to
disagree with this language particularly when you find no
actual fault with the language. I have linked to numerous
online references here; not as numerous as Lalo though. It is
almost as if you want to deny that the real numbers do fit
the ring definition.
Consider the following. Let
a_0, a_1, a_2, ... b_0, b_1, b_2, ...
be (not necessarily distinct) sequences of real numbers subject
to the requirements that only finitely many members are
non-zero.
Define the _sum_ of them to be
(a_1 + b_1), (a_2 + b_2, (a_3 + b_3), ...
And the _product_ of them to be
sum_{k=0}^infty sum_{n=0}^k a_n b_{k-n}.
I claim that the set of such sequences under sum and addition
as defined is a ring. Do you agree?
Yes or no?
No, but the problem is larger than a yes/no answer. I say yes, I see
how the polynomial products and sums work out to another polynomial;
but I say no because those sums which build the polynomial are built
via the ring operator, and the products in the terms of the
polynomial are built with that ring product, and they do not fit the
ring definition. This is not a yes/no situation. The ring of
polynomials with real coefficients is not ring behaved.
That ring is, but for notation, the same as the ring of
polynomials of one indeterminate over the real numbers denote
R[X] where R is the real numbers. The element
a_0 + a_1 X + a_2 X^2 +...
of R[X] corresponds to
a_0, a_1, a_2, ...
Do you understand that?
I understand the product and sum of polynomials and I see that at
the outer level the ring behavior is upheld but it is this method
of dismantling the polynomial which yields the conflict. Each
polynomial is a sum of terms and those terms clearly must obey the
ring definition too. Each term contains products and those products
must obey the ring definition. Otherwise there is a conflict. The
conflict is best exposed on the polynomial with real coefficients
and so to specify an instance
a1 X and witness that this product is not ring behaved;
I've asked you twice before what "ring behaved" means. Would you
like to say now? If you wish, answer with respect to a1 X rather
than generally (though generally would be best).
And yet you don't.
. But Peter if all
that we do is cover the same ground again that will not be
meaningful. You have had a chance. If all that you mean to do is
repeat the same defense then why bother? This is a big deal, so it is
worth trying again. But it is relevant to take a variation from the
prior course. In fact I am happy to expound for I think I did bump
into the reason that I use this terminology. The Ring definition is
not a concrete thing. Whereas in the definition of real numbers we
can actually name a real number 1.23 and I can comfortably say 'is
real' the ring definition really only defines requirements for
operators, and those operators perform actions. They have behavior.
They take two elements and yield one element. But furthermore there
is nothing concrete about them. Even the real value I would say is
ring behaved. To say that the real number 'is a ring' has poor
grammatical value.
Bugger its 'grammatical value', it's downright false to say that the
real number 'is a ring'. A ring is three things (S,+,*) where S is a
set and + and * are both binary operations defined on that set. Those
operations are required to satisfy certain conditions (such as
associativity) that you can look up. An example is S being the set of
real numbers and + and * being the usual arithmetical operations. To
wrote of one element of S as being a ring is silly
To say that the real number is ring behaved is
much more natural. Both I believe mean to obey the rules of the ring
definition
The definition of a ring refers to a triple, above written as (S,+,*).
It is silly to write of an element of S as obeying the rules of the ring
definition. Here's an analogy: London is defined to be the capital of
the UK (yes, I know there are other Londons but for my purposes it's
London as defined by me that I'm writing about.) Does John Smith who
lives on Eaton Square (a place in London) obey the rules of the
definition of London? No. Is that a problem? No.
You mention 1.23 X. In terms of the 'sequences of real numbers subject
to the requirements that only finitely many members are non-zero'
definition of polynomial, that is 0, 1.23, 0, 0, .... It is also the
product of 1.23, 0, 0, 0, ... and 0, 1, 0, 0, ... (Which is no more
remarkable than six being both 6 and the product of 2 and 3.)
, but the definition does not describe a set of elements;
it describes what a set of elements can do. It defines their
behavior.
that this term is in sum with other terms that will not obey the
ring definition; and of course we need just one such polynomial
to fail in order to have a falsification; one black swan proves
that not all swans are white and so we can go a bit further with
our specificity of that black swan 1.23 X which does not obey the
ring definition. This is as concrete an instance as I can muster
without breaking any of AA's rules. So there you have it: a ring
behaved polynomial that is not ring behaved. It is nice of you to
make another attempt here. For a while you were the only one who
could face the black swan. Others here have devolved into
statements like That product is not a product The sum is not a
sum Whereas the X is nearly nothing at all Were operators only
just defined in this subject Peter? The ring definition comes
some pages before the introduction of the polynomial in AA right?
Should a subject which cares to define operators use them more
carefully? Do elements contain operators? If they do then those
operators ought to resolve right? This is exactly what the AA
I don't know what 'resolve' means in this context. Nor am I sure I know
what you mean by elements containing operators. Are you taking about
the way something might be written? E.g., here's an element of the ring
of integers: 6, and it equals 2*3, and '2*3' contains the symbol '*'.
To say, instead, '6 contains *' would be potty.
polynomial does not do.
only just defined in this subject Peter? The ring definition comes
some pages before the introduction of the polynomial in AA right?
Should a subject which cares to define operators use them more
carefully? Do elements contain operators? If they do then those
operators ought to resolve right? This is exactly what the AA
polynomial does not do. Now you are dodging the black swan; something
that you used to be unafraid of. I have already conceded to you that
products of polynomials yield polynomials and sums of polynomials
yield polynomials, but my argument is on the contents of those
polynomials. I dismantle the polynomial to expose the conflict.
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
It is very clear to me that operators and elements are distinct concepts. Really they were long before their formalization in the ring definition. The polynomial simply offends this boundary. It is the fact that the polynomial is a sum of terms that allows us to dismantle it under the ring definition. Thus each term ought to be ring behaved yet for the ring of polynomials with real coefficients as we study an early term
a1 X
we see a product of two elements that does not match the ring definition. If I could state the problem more simply I would. At least in this expression we can clearly claim the elemental nature of the two parts and a sole operator of product which the expression holds. And yet the expression offends the ring definition. And now the polynomial fails term by term to meet the ring definition. There are many places where the curriculum of abstract algebra ( AA ) wheedles its way through, and as students the sole institutionalized purpose is to mimic these works. As to what sort of students such a system builds: you are a fine instance Peter. I've dug back to your earlier contributions here which ended in a claim that the black swan
1.23 X
is a matter of "pre multiplication" which is a unique interpretation. Other than this there is a failure to really sit down and have a look at the thing, and yet at that point as I recall you were the closest to it of any here. If modern mathematics holds up so well due to en masse avoidance of its issues then aren't we really practicing a religion? Why shouldn't we simply allow the analysis to take place? Instead what we see, and not just from you, is a careful dodge of the full discussion.

The full discussion I do think has to boil down to the ring's concept of elements and operators. That elements do not contain operators exposes the fraudulent use of the polynomial in abstract algebra. This then gets covered up by going over to the ordered series of coefficients and then to fully sweep the dust under the carpet an insistence on an infinite length form is made. The motivations of this last requirement have not been substantiated by anyone on this thread and I do see this as a significant point. This inverted induction technique is a matter of human behavior. It is to say that when one begins on a path of lies one is bound to have to lie again and again. Inverted induction covers that very well.

The lack of maturity in this discussion has to be exposed. The point that I make over and over again here is so simple and I do tire of making it. The black swan
1.23 X
blah blah blah... ring defintion blah blah blah... elements... blah blab blab operators.... blah blah blah closure principle...
I'm pretty sure that the advanced form of this conversation would be considerably more flexible and admit that AA has a ways to go still. It is a loose fitting form and that is the way that they like it. Yes, there are squeezes and bottlenecks that even the best professors struggle to push their students through. They've got to be very careful for some of the best will refuse to follow. I would say indeed that the very best will refuse to follow. What you wind up with on the other side is a swiss army knife. It's great for the city slicker. Need a screwdriver? No problem! Got to whittle down something? Got you covered! A bit of meat stuck in your teeth? Pull out the little white toothpick. Those tweezers are great too when you'ge gotten a splinter in your paw. And if you're heading for the woods get the one with the little saw blade to do some real work. What exactly are the actual gains from this subject? It seems that there are proofs in associative algebra that are freestanding from AA that go pretty far. I certainly am not a master of these things, but it sure would be nice to fill out the scene better than has been done here yet.

Now Peter, I have to warn you: don't get too close to the black swan. That said it's screams are far worse than its bite.
Peter
2020-10-18 15:47:06 UTC
Post by Tim Golden BandTech.com
[...]
It is very clear to me that operators and elements are distinct
concepts. Really they were long before their formalization in the
ring definition. The polynomial simply offends this boundary. It is
the fact that the polynomial is a sum of terms that allows us to
dismantle it under the ring definition. Thus each term ought to be
ring behaved yet for the ring of polynomials with real coefficients
as we study an early term > a1 X
we see a product of two elements that
does not match the ring definition.
Using the "sequences of numbers only finitely many not 0" definition of
polynomial, we see that

a1 is the sequence a1, 0, 0, ..., and
X is the sequence 0, 1, 0, ...

the product of which is 0, a1, 0, ...

(In all cases "..." indicates an infinity of 0s.)
Post by Tim Golden BandTech.com
If I could state the problem more
simply I would. At least in this expression we can clearly claim the
elemental nature of the two parts and a sole operator of product
which the expression holds. And yet the expression offends the ring
definition. And now the polynomial fails term by term to meet the
ring definition. There are many places where the curriculum of
abstract algebra ( AA ) wheedles its way through, and as students the
sole institutionalized purpose is to mimic these works. As to what
sort of students such a system builds: you are a fine instance Peter.
I've dug back to your earlier contributions here which ended in a
claim that the black swan 1.23 X is a matter of "pre multiplication"
I think my use of the word "pre multiplication" has mislead you. In
2*3, 2 is said to pre multiply 3. Nothing more than that. Please put
Post by Tim Golden BandTech.com
which is a unique interpretation. Other than this there is a failure
to really sit down and have a look at the thing, and yet at that
point as I recall you were the closest to it of any here. If modern
mathematics holds up so well due to en masse avoidance of its issues
then aren't we really practicing a religion? Why shouldn't we simply
allow the analysis to take place? Instead what we see, and not just
from you, is a careful dodge of the full discussion.
Any algebra text will have this result: start with a ring R, define a
structure, usually denoted R[X], which is a set furnished with two
structure so defined is a ring. If you were to read such a text (I'm
confident you won't) one of two things would be the case - either you
would understand it and see that it is correct, or you would not
understand it. In the second case you would conclude, not that you
didn't understand it, but that it was wrong.

For you, R is the real numbers which is why I wrote above "sequences of
_numbers_ only finitely many not 0" (emphasis added). Generally, it's
not numbers, but elements of the ring R.

I have never tried laying bricks. My guess is, that if I did so I would
be hopeless at it. Suppose that were so. I would *not* conclude that
something was wrong with the bricks or the cement. I would conclude
that bricklaying was not for me. That way of thinking is not available
to you. I don't know why.
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
Lalo T.
2020-10-18 23:53:14 UTC
https://en.wikipedia.org/wiki/Basis_(linear_algebra)#Examples
https://en.wikipedia.org/wiki/Monomial_basis

https://math.stackexchange.com/questions/2357713/polynomials-indeterminate
https://math.stackexchange.com/questions/579441/determining-whether-given-polynomials-form-a-basis
https://math.stackexchange.com/questions/1271389/polynomial-maps-on-indeterminate-of-vector-space-of-polynomials

in Numerical Polynomial Algebra by Hans J. Stetter
https://www.amazon.com/Numerical-Polynomial-Algebra-Hans-Stetter/dp/0898715571
the author, besides some remarks in polynomial related concepts, also has a
subsection on floating point arithmetic (upthread you mention the topic of
polynomial in the context of positional number system)

In any case, you could ask in several forums (mainstream or specialized)
how the terminology in engendered/produced, and what terminology is useful
and what terminology is misleading. I guess, alternatively, you can email some

What is required to know what names/concepts are misleading, and
what names/concepts are actually useful?

What is "indeterminate" here ?

What notation is more like the Horsey Horseless ?

What mathematical concepts can be formulated before your central critique arise,
and what concepts can be formulated after your central critique arise ?
(central critique = black swan)

In what degrees of complexity and rigour are used (or not used) certain words ?

How one can know if the words used so far in the thread are protection from
disproportionate and unnecessary complexity ?

Do you want search the truth only in the confines of online PDFs and
Scimath ?

https://www-cs-faculty.stanford.edu/~knuth/email.html
http://www.kurims.kyoto-u.ac.jp/~motizuki/top-english.html

Actually, a few authors will take the time to reply questions if you email them.
if you know how to contact, some author may repply...
(through email, hand-written correspondence, fax or social network groups)

You may end up writing :
'The truth behind polynomials and indeterminates, The ultimate book'

Certainly, I am not sure in recommending you the use the terminology of
"signed set" and "gradation" with the same meanings as is used in :

https://en.wikipedia.org/wiki/Signed_set

which may resemble some of what you are referring with Polysign,
but you will have to examine if the meanings are imbued/immersed in the

Always is tempting (and a good practice) to re-use/recycle as much as possible.
An example of this could be the use of modular arithmetic and Congruence classes

" In mathematics, modular arithmetic is a system of arithmetic for integers,.. "
in https://en.wikipedia.org/wiki/Modular_arithmetic

a ~ b ≡ c (mod 8)
7 ~ 2 ≡ 5 (mod 8)
2 ~ 7 ≡ 3 (mod 8)
3 ≢ 5 (mod 8)

A very tiny part of the motivation of the way how the Algebra Tree grow, so to
speak, is because is "non-compartimentalized". Since it was built that way
in an early stage of development, and know that the Tree is in adult stage,
to what degree can I recycle machinery and resources to not re-invent the
wheel ?

To what degree is convenient to re-use already used word ?

how would be the concept of basis(linear algebra) in the style of your system ?

signum( object ) ✖ length( object ) <--> object ???

< ... http://iconicmath.com/algebra/james/

< shows the unsigned value has a more fundamental status.
I would wonder how you would explain the usage of the word "unsigned" to
a person that think "unsigned" = "positive"...

< But there is no usage of an origin in his work that I have seen
Does he use the "sign" only in the context of operation addition/subtraction?
Does he use the concept of zero ?

is the zero concept necessarily tied with positional number systems ?

how can one prescind the usage of zero in the context of null terms ?

a + b + c + d + f
a + b + c + d + f + ∅ + ∅ + ∅ + ∅ ....
a + b + ∅ + d + f
a + b + d + f

Will you reserve a bit specially for zero or keep the info of zero in the
magnitude part ?
Tim Golden BandTech.com
2020-10-19 13:03:57 UTC
Post by Lalo T.
https://en.wikipedia.org/wiki/Basis_(linear_algebra)#Examples
https://en.wikipedia.org/wiki/Monomial_basis
https://math.stackexchange.com/questions/2357713/polynomials-indeterminate
https://math.stackexchange.com/questions/579441/determining-whether-given-polynomials-form-a-basis
https://math.stackexchange.com/questions/1271389/polynomial-maps-on-indeterminate-of-vector-space-of-polynomials
in Numerical Polynomial Algebra by Hans J. Stetter
https://www.amazon.com/Numerical-Polynomial-Algebra-Hans-Stetter/dp/0898715571
the author, besides some remarks in polynomial related concepts, also has a
subsection on floating point arithmetic (upthread you mention the topic of
polynomial in the context of positional number system)
In any case, you could ask in several forums (mainstream or specialized)
how the terminology in engendered/produced, and what terminology is useful
and what terminology is misleading. I guess, alternatively, you can email some
Yeah, well, in a polite tone I can get nowhere on this issue. That is a guarantee.
All that you will get back is the same regurgitation that has been going on here.
Post by Lalo T.
What is required to know what names/concepts are misleading, and
what names/concepts are actually useful?
What is "indeterminate" here ?
Really. Is X in abstract algebra indeterminate or is it even less than indeterminate? If its qualities have not been fully categorized then what exactly is it? This discussion again is not had in the texts of abstract algebra. To say that this is tender ground.... now why would that be?
Could it be that the familiarity with the x in the polynomial of childhood is misleading? As far as I can tell none of this gets discussed. It is obfuscated.
Post by Lalo T.
What notation is more like the Horsey Horseless ?
What mathematical concepts can be formulated before your central critique arise,
and what concepts can be formulated after your central critique arise ?
(central critique = black swan)
In what degrees of complexity and rigour are used (or not used) certain words ?
How one can know if the words used so far in the thread are protection from
disproportionate and unnecessary complexity ?
Do you want search the truth only in the confines of online PDFs and
Scimath ?
https://www-cs-faculty.stanford.edu/~knuth/email.html
http://www.kurims.kyoto-u.ac.jp/~motizuki/top-english.html
Actually, a few authors will take the time to reply questions if you email them.
if you know how to contact, some author may repply...
(through email, hand-written correspondence, fax or social network groups)
'The truth behind polynomials and indeterminates, The ultimate book'
Certainly, I am not sure in recommending you the use the terminology of
https://en.wikipedia.org/wiki/Signed_set
which may resemble some of what you are referring with Polysign,
but you will have to examine if the meanings are imbued/immersed in the
Always is tempting (and a good practice) to re-use/recycle as much as possible.
An example of this could be the use of modular arithmetic and Congruence classes
" In mathematics, modular arithmetic is a system of arithmetic for integers,.. "
in https://en.wikipedia.org/wiki/Modular_arithmetic
a ~ b ≡ c (mod 8)
7 ~ 2 ≡ 5 (mod 8)
2 ~ 7 ≡ 3 (mod 8)
3 ≢ 5 (mod 8)
A very tiny part of the motivation of the way how the Algebra Tree grow, so to
speak, is because is "non-compartimentalized". Since it was built that way
in an early stage of development, and know that the Tree is in adult stage,
to what degree can I recycle machinery and resources to not re-invent the
wheel ?
To what degree is convenient to re-use already used word ?
how would be the concept of basis(linear algebra) in the style of your system ?
signum( object ) ✖ length( object ) <--> object ???
< ... http://iconicmath.com/algebra/james/
< shows the unsigned value has a more fundamental status.
I would wonder how you would explain the usage of the word "unsigned" to
a person that think "unsigned" = "positive"...
< But there is no usage of an origin in his work that I have seen
Does he use the "sign" only in the context of operation addition/subtraction?
Does he use the concept of zero ?
is the zero concept necessarily tied with positional number systems ?
how can one prescind the usage of zero in the context of null terms ?
You know this is another fine criticism of AA though it feels like we're just making fun of them. To them when I mention the black swan
1.23 X
their immediate first thought is : 'where are all the zero terms?' This is the sort of silliness that is required; for some there must be an infinite length of zero terms attached to this construction above. It proves nothing, but it indicates what a farce AA is. As to who is performing via diversionary tactics here; who is being as direct as possible here; certainly I do use quite a lot of rhetoric and this is no place to be polite; but on content I will have to hope that an onlooker, whether bot or human, will get a clean measurement.
Post by Lalo T.
a + b + c + d + f
a + b + c + d + f + ∅ + ∅ + ∅ + ∅ ....
a + b + ∅ + d + f
a + b + d + f
Will you reserve a bit specially for zero or keep the info of zero in the
magnitude part ?
Tim Golden BandTech.com
2020-10-19 13:45:49 UTC
Post by Lalo T.
< ... http://iconicmath.com/algebra/james/
No me either. It's a whacky site. It almost looks hacked. I did find this starting place though

http://iconicmath.com/mypdfs/james-algebra.120909.pdf
Lalo T.
2020-10-19 21:03:18 UTC
I imagine that you do not want this following type of answer :

" To make this completely formal without having to worry about what the
variable x means... "
https://math.stackexchange.com/questions/216470/what-is-a-formal-polynomial

" Likewise, the polynomial ring may be regarded as a "free commutative algebra" "
in https://en.wikipedia.org/wiki/Free_algebra
https://planetmath.org/FreeCommutativeAlgebra

" f R is commutative, the polynomial ring R[X] in indeterminate X is a
free module with a possible basis 1,X,X²,.. "
in https://en.wikipedia.org/wiki/Free_module#Examples
"formal linear combination"
in https://math.stackexchange.com/questions/996556/why-formal-linear-combination

https://en.wikipedia.org/wiki/Group_ring#Examples
note C[a]/(a³-1) VS C[a]/(a²+a+1) VS C[a]/(a²+1)

https://en.wikipedia.org/wiki/Indeterminate_(variable)#As_generators

https://en.wikipedia.org/wiki/Monomial_basis

https://en.wikipedia.org/wiki/Free_monoid#The_free_commutative_monoid

https://en.wikipedia.org/wiki/Indeterminate_(variable)#As_generators

https://en.wikipedia.org/wiki/Generator_(mathematics)

" Algebraists employ formal (vs. functional) polynomials because this yields
the greatest generality. "
https://math.stackexchange.com/questions/98345/why-are-polynomials-defined-to-be-formal-vs-functions

" Said informally, R[x] is the "freest" possible ring obtained by hypothesizing
only that it is a ring "
in https://math.stackexchange.com/questions/157047/axiomatic-approach-to-polynomials

https://commalg.subwiki.org/wiki/Polynomial_ring#Extra_structure

But, it depends on your view and philosophy that you have on
the use of certain abstract areas of mathematics

" Universal algebra (sometimes called general algebra) is the field of
mathematics that studies algebraic structures themselves, not examples
("models") of algebraic structures. For instance, rather than take particular
groups as the object of study, in universal algebra one takes the class of
groups as an object of study. "
https://en.wikipedia.org/wiki/Universal_algebra#History

by the way, you mentioned Chomsky upthread
https://en.wikipedia.org/wiki/Pirah%C3%A3_language#Unusual_features_of_the_language
https://en.wikipedia.org/wiki/Cyclic_language

How would be the concept of Linear Span in a polysign-like algebra ?
https://en.wikipedia.org/wiki/Linear_span#Examples
Tim Golden BandTech.com
2020-10-19 12:45:33 UTC
Post by Peter
Post by Tim Golden BandTech.com
[...]
It is very clear to me that operators and elements are distinct
concepts. Really they were long before their formalization in the
ring definition. The polynomial simply offends this boundary. It is
the fact that the polynomial is a sum of terms that allows us to
dismantle it under the ring definition. Thus each term ought to be
ring behaved yet for the ring of polynomials with real coefficients
as we study an early term > a1 X
we see a product of two elements that
does not match the ring definition.
Using the "sequences of numbers only finitely many not 0" definition of
polynomial, we see that
a1 is the sequence a1, 0, 0, ..., and
X is the sequence 0, 1, 0, ...
the product of which is 0, a1, 0, ...
(In all cases "..." indicates an infinity of 0s.)
Post by Tim Golden BandTech.com
If I could state the problem more
simply I would. At least in this expression we can clearly claim the
elemental nature of the two parts and a sole operator of product
which the expression holds. And yet the expression offends the ring
definition. And now the polynomial fails term by term to meet the
ring definition. There are many places where the curriculum of
abstract algebra ( AA ) wheedles its way through, and as students the
sole institutionalized purpose is to mimic these works. As to what
sort of students such a system builds: you are a fine instance Peter.
I've dug back to your earlier contributions here which ended in a
claim that the black swan 1.23 X is a matter of "pre multiplication"
I think my use of the word "pre multiplication" has mislead you. In
2*3, 2 is said to pre multiply 3. Nothing more than that. Please put
Post by Tim Golden BandTech.com
which is a unique interpretation. Other than this there is a failure
to really sit down and have a look at the thing, and yet at that
point as I recall you were the closest to it of any here. If modern
mathematics holds up so well due to en masse avoidance of its issues
then aren't we really practicing a religion? Why shouldn't we simply
allow the analysis to take place? Instead what we see, and not just
from you, is a careful dodge of the full discussion.
Any algebra text will have this result: start with a ring R, define a
structure, usually denoted R[X], which is a set furnished with two
structure so defined is a ring. If you were to read such a text (I'm
confident you won't) one of two things would be the case - either you
would understand it and see that it is correct, or you would not
understand it. In the second case you would conclude, not that you
didn't understand it, but that it was wrong.
For you, R is the real numbers which is why I wrote above "sequences of
_numbers_ only finitely many not 0" (emphasis added). Generally, it's
not numbers, but elements of the ring R.
I have never tried laying bricks. My guess is, that if I did so I would
be hopeless at it. Suppose that were so. I would *not* conclude that
something was wrong with the bricks or the cement. I would conclude
that bricklaying was not for me. That way of thinking is not available
to you. I don't know why.
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
So it looks to me at though in dodging the X polynomial format you are admitting that it has weakness. That the ordered form has perfect equivalence does nothing to protect your argument. You are merely distancing yourself from a problem. Beyond this simple conflict lays a trove of possibly interpretations. Some here have gone so far as to claim that the sum in the polynomial is not actually a sum, and others state that the product in the polynomial is not a product. By making the X, the sum, and the product disappear you are certainly disowning the polynomial form. Thank you Peter for exposing the flaws in this mathematics even while you cannot state the problem. Such interpretations act as a straightjacket, and this is exactly as I see the academic system. That you cannot come clean on the black swan
1.23 X
is perfect positioning as far as I can tell. That a ring behaved system is a long sum of such terms; this implies then that each term is ring behaved. That this is as concrete a term as we can have in the ring of polynomials with real coefficients; one of the simplest forms that this math works from; which fails the ring requirements and so cannot be ring behaved... Thank you for dodging the argument completely.
Peter
2020-10-19 23:21:55 UTC
Post by Tim Golden BandTech.com
Post by Peter
Post by Tim Golden BandTech.com
[...]
It is very clear to me that operators and elements are distinct
concepts. Really they were long before their formalization in the
ring definition. The polynomial simply offends this boundary. It is
the fact that the polynomial is a sum of terms that allows us to
dismantle it under the ring definition. Thus each term ought to be
ring behaved yet for the ring of polynomials with real coefficients
as we study an early term > a1 X
we see a product of two elements that
does not match the ring definition.
Using the "sequences of numbers only finitely many not 0" definition of
polynomial, we see that
a1 is the sequence a1, 0, 0, ..., and
X is the sequence 0, 1, 0, ...
the product of which is 0, a1, 0, ...
(In all cases "..." indicates an infinity of 0s.)
Post by Tim Golden BandTech.com
If I could state the problem more
simply I would. At least in this expression we can clearly claim the
elemental nature of the two parts and a sole operator of product
which the expression holds. And yet the expression offends the ring
definition. And now the polynomial fails term by term to meet the
ring definition. There are many places where the curriculum of
abstract algebra ( AA ) wheedles its way through, and as students the
sole institutionalized purpose is to mimic these works. As to what
sort of students such a system builds: you are a fine instance Peter.
I've dug back to your earlier contributions here which ended in a
claim that the black swan 1.23 X is a matter of "pre multiplication"
I think my use of the word "pre multiplication" has mislead you. In
2*3, 2 is said to pre multiply 3. Nothing more than that. Please put
Post by Tim Golden BandTech.com
which is a unique interpretation. Other than this there is a failure
to really sit down and have a look at the thing, and yet at that
point as I recall you were the closest to it of any here. If modern
mathematics holds up so well due to en masse avoidance of its issues
then aren't we really practicing a religion? Why shouldn't we simply
allow the analysis to take place? Instead what we see, and not just
from you, is a careful dodge of the full discussion.
Any algebra text will have this result: start with a ring R, define a
structure, usually denoted R[X], which is a set furnished with two
structure so defined is a ring. If you were to read such a text (I'm
confident you won't) one of two things would be the case - either you
would understand it and see that it is correct, or you would not
understand it. In the second case you would conclude, not that you
didn't understand it, but that it was wrong.
For you, R is the real numbers which is why I wrote above "sequences of
_numbers_ only finitely many not 0" (emphasis added). Generally, it's
not numbers, but elements of the ring R.
I have never tried laying bricks. My guess is, that if I did so I would
be hopeless at it. Suppose that were so. I would *not* conclude that
something was wrong with the bricks or the cement. I would conclude
that bricklaying was not for me. That way of thinking is not available
to you. I don't know why.
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
So it looks to me at though in dodging the X polynomial format you are admitting that it has weakness. That the ordered form has perfect equivalence does nothing to protect your argument. You are merely distancing yourself from a problem. Beyond this simple conflict lays a trove of possibly interpretations. Some here have gone so far as to claim that the sum in the polynomial is not actually a sum, and others state that the product in the polynomial is not a product. By making the X, the sum, and the product disappear you are certainly disowning the polynomial form. Thank you Peter for exposing the flaws in this mathematics even while you cannot state the problem. Such interpretations act as a straightjacket, and this is exactly as I see the academic system. That you cannot come clean on the black swan
1.23 X
is perfect positioning as far as I can tell. That a ring behaved system is a long sum of such terms; this implies then that each term is ring behaved. That this is as concrete a term as we can have in the ring of polynomials with real coefficients; one of the simplest forms that this math works from; which fails the ring requirements and so cannot be ring behaved... Thank you for dodging the argument completely.
I pointed out in an earlier post that there is a correspondence between
the X format and the sequence format. Anyone who knows a little algebra
can switch back and forth between them with ease. But if one of them
troubles you then don't use it, just use the other one.

On 17/10/2020 15:44 BST I asked:

The element

a_0 + a_1 X + a_2 X^2 +...

of R[X] corresponds to

a_0, a_1, a_2, ...

Do you understand that?
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
Peter
2020-10-20 01:23:24 UTC
Post by Peter
Post by Tim Golden BandTech.com
Post by Peter
Post by Tim Golden BandTech.com
[...]
It is very clear to me that operators and elements are distinct
concepts. Really they were long before their formalization in the
ring definition. The polynomial simply offends this boundary. It is
the fact that the polynomial is a sum of terms that allows us to
dismantle it under the ring definition. Thus each term ought to be
ring behaved yet for the ring of polynomials with real coefficients
as we study an early term > a1 X
we see a product of two elements that
does not match the ring definition.
Using the "sequences of numbers only finitely many not 0" definition of
polynomial, we see that
a1 is the sequence a1, 0, 0, ..., and
X is the sequence 0, 1, 0, ...
the product of which is 0, a1, 0, ...
(In all cases "..." indicates an infinity of 0s.)
Post by Tim Golden BandTech.com
If I could state the problem more
simply I would. At least in this expression we can clearly claim the
elemental nature of the two parts and a sole operator of product
which the expression holds. And yet the expression offends the ring
definition. And now the polynomial fails term by term to meet the
ring definition. There are many places where the curriculum of
abstract algebra ( AA ) wheedles its way through, and as students the
sole institutionalized purpose is to mimic these works. As to what
sort of students such a system builds: you are a fine instance Peter.
I've dug back to your earlier contributions here which ended in a
claim that the black swan 1.23 X is a matter of "pre multiplication"
I think my use of the word "pre multiplication" has mislead you. In
2*3, 2 is said to pre multiply 3. Nothing more than that. Please put
Post by Tim Golden BandTech.com
which is a unique interpretation. Other than this there is a failure
to really sit down and have a look at the thing, and yet at that
point as I recall you were the closest to it of any here. If modern
mathematics holds up so well due to en masse avoidance of its issues
then aren't we really practicing a religion? Why shouldn't we simply
allow the analysis to take place? Instead what we see, and not just
from you, is a careful dodge of the full discussion.
Any algebra text will have this result: start with a ring R, define a
structure, usually denoted R[X], which is a set furnished with two
structure so defined is a ring. If you were to read such a text (I'm
confident you won't) one of two things would be the case - either you
would understand it and see that it is correct, or you would not
understand it. In the second case you would conclude, not that you
didn't understand it, but that it was wrong.
For you, R is the real numbers which is why I wrote above "sequences of
_numbers_ only finitely many not 0" (emphasis added). Generally, it's
not numbers, but elements of the ring R.
I have never tried laying bricks. My guess is, that if I did so I would
be hopeless at it. Suppose that were so. I would *not* conclude that
something was wrong with the bricks or the cement. I would conclude
that bricklaying was not for me. That way of thinking is not available
to you. I don't know why.
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
So it looks to me at though in dodging the X polynomial format you are
admitting that it has weakness. That the ordered form has perfect
equivalence does nothing to protect your argument. You are merely
distancing yourself from a problem.  Beyond this simple conflict lays
a trove of possibly interpretations. Some here have gone so far as to
claim that the sum in the polynomial is not actually a sum, and others
state that the product in the polynomial is not a product. By making
the X, the sum, and the product disappear you are certainly disowning
the polynomial form. Thank you Peter for exposing the flaws in this
mathematics even while you cannot state the problem. Such
interpretations act as a straightjacket, and this is exactly as I see
the academic system. That you cannot come clean on the black swan
1.23 X
is perfect positioning as far as I can tell. That a ring behaved
system is a long sum of such terms; this implies then that each term
is ring behaved. That this is as concrete a term as we can have in the
ring of polynomials with real coefficients; one of the simplest forms
that this math works from; which fails the ring requirements and so
cannot be ring behaved... Thank you for dodging the argument completely.
I pointed out in an earlier post that there is a correspondence between
the X format and the sequence format.  Anyone who knows a little algebra
can switch back and forth between them with ease.  But if one of them
troubles you then don't use it, just use the other one.
The element
a_0 + a_1 X + a_2 X^2 +...
of R[X] corresponds to
Is would have been better if I had written "is" rather than
"corresponds", just a 5+1 _is_ 6.
Post by Peter
a_0, a_1, a_2, ...
Do you understand that?
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
zelos...@gmail.com
2020-10-19 04:54:29 UTC
I understand the product and sum of polynomials and I see that at the outer level the ring behavior is upheld but it is this method of dismantling the polynomial which yields the conflict
There is no conflict, only you conflating notation with what things actually are.
Each polynomial is a sum of terms and those terms clearly must obey the ring definition too.
And here you demonstrate it

When we write a_0+a_1*x^1+a_2*x^2+...+a_n*x^n

Thats not a fucking sum nor any products, it is NOTATION for polynomial that comes from history.

The formal definition have no internal sums or products other than the sum of polynomials and product of them. How difficult is this to fucking understand?
Each term contains products and those products must obey the ring definition.
Except in the formal construction THERE ARE NO FUCKING TERMS OR PRODUCTS THAT YOU SPEAK OF!
zelos...@gmail.com
2020-10-19 04:59:00 UTC
Post by Lalo T.
https://en.wikipedia.org/wiki/Basis_(linear_algebra)
https://en.wikipedia.org/wiki/Quaternion_group#Matrix_representations
https://mathworld.wolfram.com/QuaternionGroup.html
https://en.wikipedia.org/wiki/Classical_Hamiltonian_quaternions#Division_of_the_unit_vectors_i,_j,_k
In real numbers, how can '-' with '1' in the expression '-1' evaluate (or not
evaluate), and in quaternions, the case for '-5' with 'j' in '-5j' evaluate (or
not evaluate) if, they are not separated in the first place ?
In the case of Complex numbers, if more noticeable (again) if a
https://en.wikipedia.org/wiki/Quater-imaginary_base
https://en.wikipedia.org/wiki/Balanced_ternary
From the algebraic perspective, you could do a version of Complex Numbers
or Quaternions (or any orthogonal number system) in your style, this is,
with differentiation/compartmentalization of the 'sign component' respect to the
'length component' (and keeping the orthogonal feature)
( "Direction Algebra" separated from the "Length Algebra", so to speak )
Conventional Algebra (abstract or not) have to choose some element.
It cannot take, what you call in your system, the 'sign component', as
distinguished from the 'magnitude component' (in a "term").
Roger Beresford use what he calls 'primal numbers', but, it could be checked
if he uses the 'sign part' (in the meaning as you use it), or he just leverage
on "elements that spin", since he uses terminology of Algebra.
What is a Vector Space ?
Vector spaces are well behaved under addition. This couples really to your concern on subtraction in a prior post. There is no need for subtraction as a fundamental operation. Of course within AA this is exposed in the ring definition. If you have an inverse than you can have subtraction, but it is merely the sum of the inverse.When you start graphing these on paper you will have a good sense of a vector space.
Vectors carry very good physical correspondence. Traditionally 3D space is done with three orthogonal real lines. P4 covers it with just four rays; whereas the Cartesian tradition requires six. Six directions of space or four? If it can be done in four then the 'real' answer is four.
Post by Lalo T.
If your system (polysigns) is correct, then, the incorrect thing, from my
perspective, would be try to judge if two things evaluate (or not evaluate),
when they are not two different things in the first place.
In two different algebras, as in two different tongues, the sentences are
structured differently...
P1 P2 P3 P4 P5 P6 ... Pn ?
If you say there are n tongues then so be it. But if you say there is one tongue then there is no new language present, for P2 are the real numbers. We can only lean on this language paradigm so far. It's clean math and you know it. I have no idea why you run at the mouth here so insincerely. I would rather have a sincere conversation. There is no fog present in the polysign numbers. They are pristine.
https://proofwiki.org/wiki/Definition:Polynomial_Ring

Notice how polynomial rings are not defined/constructed as sums/products of anything you imbecile?
Tim Golden BandTech.com
2020-10-19 13:12:51 UTC
Post by ***@gmail.com
https://proofwiki.org/wiki/Definition:Polynomial_Ring
This is definitely a bogus definition.
This construction as it is written there now will not stand.
X as an element of the ring while XX is not an element of the ring is the fail point. This will likewise cause the ordered series to fail. Of course the ordered series has been an escape mechanism for a long time in mathematics. It is handy, but the misuse of it only encourages more misuse of it. I tend to do this interpretation in terms of dimensional analysis, but I'm sure others will find the same from straight set theory. So it is that this attack forms an attack on the ordered series representation within AA to claim one ring to be an infinity of unique such rings under your own insistence. Really I'm sorry but once you allow your skepticism to creep into this subject the whole mess falls apart.

Zelos you should be a special character hiding in the shadows of the bridge. You have ring that you call precious...
zelos...@gmail.com
2020-10-20 05:48:41 UTC
Post by Tim Golden BandTech.com
Post by ***@gmail.com
https://proofwiki.org/wiki/Definition:Polynomial_Ring
This is definitely a bogus definition.
This construction as it is written there now will not stand.
X as an element of the ring while XX is not an element of the ring is the fail point. This will likewise cause the ordered series to fail. Of course the ordered series has been an escape mechanism for a long time in mathematics. It is handy, but the misuse of it only encourages more misuse of it. I tend to do this interpretation in terms of dimensional analysis, but I'm sure others will find the same from straight set theory. So it is that this attack forms an attack on the ordered series representation within AA to claim one ring to be an infinity of unique such rings under your own insistence. Really I'm sorry but once you allow your skepticism to creep into this subject the whole mess falls apart.
Zelos you should be a special character hiding in the shadows of the bridge. You have ring that you call precious...
Those are the correct FORMAL definitions. Which is why I say your complaints are INVALID
Lalo T.
2020-10-20 08:04:52 UTC
z₁ = (-a @ +b @ *c)

reciprocal of z₁
(*1) / (z₁) = (*1) / (-a @ +b @ *c) = ??

z₂ = (+a @ -b @ *c)
z₃ = (*a @ *b @ *c)

(*1) / z₁ = ( (*1)(z2)(z3) ) / ( (-a @ +b @ *c)(z2)(z3) )

(z₂)(z₃) = +a² @ -b² @ *c² @ -ab @ +ab @ +ac @ *ac @ -bc @ *bc

(z₁)(z₂)(z₃) = *a³ @ *b³ @ *c³ @ -3abc @ +3abc

ex :

z₁ = (-2 @ +3 @ *5)

(z₂)(z₃) = +2² @ -3² @ *5⁵ @ -(2·3) @ +(2·3) @ +(2·5) @ *(2·5) @ -(3·5) @ *(3·5)
(z₂)(z₃) = +4 @ -9 @ *25 @ -6 @ +6 @ +10 @ *10 @ -15 @ *15
(z₂)(z₃) = (-9 @ -6 @ -15) @ (+4 @ +6 @ +10) @ (*25 @ *10 @ *15)
(z₂)(z₃) = -30 @ +20 @ *50

(z₁)(z₂)(z₃) = *2³ @ *3³ @ *5³ @ -(3·2·3·5) @ +(3·2·3·5)
(z₁)(z₂)(z₃) = *8 @ *27 @ *125 @ -90 @ +90
(z₁)(z₂)(z₃) = *160 @ -90 @ +90
(z₁)(z₂)(z₃) = *70

( (z₂)(z₃) )/( (z₁)(z₂)(z₃) ) = (-30)/(*70) @ (+20)/(*70) @ (*50)/(*70)
( (z₂)(z₃) )/( (z₁)(z₂)(z₃) ) =?= -(3/7) @ +(2/7) @ *(5/7) = w

(z₁)(w) = (-2 @ +3 @ *5)( -³/₇ @ +²/₇ @ *⁵/₇ )
(z₁)(w) = +⁶/₇ @ *⁴/₇ @ -¹⁰/₇ @ *⁹/₇ @ -⁶/₇ @ +¹⁵/₇ @ -¹⁵/₇ @ +¹⁰/₇ @ *²⁵/₇
(z₁)(w) = (-¹⁰/₇ @ -⁶/₇ @ -¹⁵/₇) @ (+⁶/₇ @ +¹⁵/₇ @ +¹⁰/₇) @ (*⁴/₇ @ *⁹/₇ @ *²⁵/₇)
(z₁)(w) = -³¹/₇ @ +³¹/₇ @ *³⁸/₇
(z₁)(w) = -³¹/₇ @ +³¹/₇ @ *³¹/₇ @ *⁷/₇
(z₁)(w) = *⁷/₇ = *1

I do not know which form would be, keep it as reciprocal of a sum, or,
send the information to th
Tim Golden BandTech.com
2020-10-20 14:44:59 UTC
Post by Lalo T.
reciprocal of z₁
(z₁)(z₂)(z₃) = *70
(z₁)(w) = *⁷/₇ = *1
I do not know which form would be, keep it as reciprocal of a sum, or,
send the information to the length-component.
Nicely done. Looking at it after the fact it seems clear. And it is going to work at least partially in higher sign. It's a bit like going back to your map of the signs on a wheel.
z1 z2 = ( - a + b * c )( - b + a * c ) = + ab * aa - ac * bb - ab + bc - bc + ac * cc = - ab - ac - bc + ab + ac + bc * aa * bb * cc
I see it doesn't really cancel at this point, but it does have the symmetry.
z3z12z2 = ( * a * b * c )( + ab * aa - ac * bb - ab + bc - bc + ac * cc ) =
= + aab * aaa - aac * abb -aab + abc ...
Geeze. 27 terms here! And that's just P3... This is some grand cancellation. I've got to do it.
Using a text editor with search and replace I've gotten
=
+ aab * aaa - aac * abb - aab + abc - abc + aac * acc
+ bab * baa - bac * bbb - bab + bbc - bbc + bac * bcc
+ cab * caa - cac * cbb - cab + cbc - cbc + cac * ccc

and now using insertion mode of text editor manually searching terms for cancellation (leaving signs for confirmation initially)

= [elim aab]
* aaa - aac * abb + abc - abc + aac * acc
+ bab - bac * bbb - bab + bbc - bbc + bac * bcc
+ cab * caa - cac * cbb - cab + cbc - cbc + cac * ccc

= [elim aac]
* aaa * abb + abc - abc * acc
+ bab - bac * bbb - bab + bbc - bbc + bac * bcc
+ cab - cac * cbb - cab + cbc - cbc + cac * ccc

= [elim abb]
* aaa + abc - abc * acc
- bac * bbb + bbc - bbc + bac * bcc
+ cab - cac * cbb - cab + cbc - cbc + cac * ccc

= [elim acc]
* aaa + abc - abc
- bac * bbb + bbc - bbc + bac * bcc
+ cab * cbb - cab + cbc - cbc * ccc

= [elim bbc]
* aaa + abc - abc
- bac * bbb + bac * bcc
+ cab - cab + cbc - cbc * ccc

= [elim bcc]
* aaa + abc - abc
- bac * bbb + bac
+ cab - cab * ccc

= [done elim]
* aaa * bbb * ccc + abc + bac + cab - abc - bac - cab
= * aaa * bbb * ccc + 3abc - 3abc

Thank you very little google for allowing the usage of a fixed width font here. Maybe it looks better on a proper usenet server.
It looks like there is still quite a bit to discuss. Side effects are of great interest.

So Lalo Torres has the first native reciprocal or conjugate of P3 polysign. Congratulations. Wow.
zelos...@gmail.com
2020-10-21 07:56:50 UTC
Post by Tim Golden BandTech.com
Post by Lalo T.
reciprocal of z₁
(z₁)(z₂)(z₃) = *70
(z₁)(w) = *⁷/₇ = *1
I do not know which form would be, keep it as reciprocal of a sum, or,
send the information to the length-component.
Nicely done. Looking at it after the fact it seems clear. And it is going to work at least partially in higher sign. It's a bit like going back to your map of the signs on a wheel.
z1 z2 = ( - a + b * c )( - b + a * c ) = + ab * aa - ac * bb - ab + bc - bc + ac * cc = - ab - ac - bc + ab + ac + bc * aa * bb * cc
I see it doesn't really cancel at this point, but it does have the symmetry.
z3z12z2 = ( * a * b * c )( + ab * aa - ac * bb - ab + bc - bc + ac * cc ) =
= + aab * aaa - aac * abb -aab + abc ...
Geeze. 27 terms here! And that's just P3... This is some grand cancellation. I've got to do it.
Using a text editor with search and replace I've gotten
=
+ aab * aaa - aac * abb - aab + abc - abc + aac * acc
+ bab * baa - bac * bbb - bab + bbc - bbc + bac * bcc
+ cab * caa - cac * cbb - cab + cbc - cbc + cac * ccc
and now using insertion mode of text editor manually searching terms for cancellation (leaving signs for confirmation initially)
= [elim aab]
* aaa - aac * abb + abc - abc + aac * acc
+ bab - bac * bbb - bab + bbc - bbc + bac * bcc
+ cab * caa - cac * cbb - cab + cbc - cbc + cac * ccc
= [elim aac]
* aaa * abb + abc - abc * acc
+ bab - bac * bbb - bab + bbc - bbc + bac * bcc
+ cab - cac * cbb - cab + cbc - cbc + cac * ccc
= [elim abb]
* aaa + abc - abc * acc
- bac * bbb + bbc - bbc + bac * bcc
+ cab - cac * cbb - cab + cbc - cbc + cac * ccc
= [elim acc]
* aaa + abc - abc
- bac * bbb + bbc - bbc + bac * bcc
+ cab * cbb - cab + cbc - cbc * ccc
= [elim bbc]
* aaa + abc - abc
- bac * bbb + bac * bcc
+ cab - cab + cbc - cbc * ccc
= [elim bcc]
* aaa + abc - abc
- bac * bbb + bac
+ cab - cab * ccc
= [done elim]
* aaa * bbb * ccc + abc + bac + cab - abc - bac - cab
= * aaa * bbb * ccc + 3abc - 3abc
Thank you very little google for allowing the usage of a fixed width font here. Maybe it looks better on a proper usenet server.
It looks like there is still quite a bit to discuss. Side effects are of great interest.
So Lalo Torres has the first native reciprocal or conjugate of P3 polysign. Congratulations. Wow.
why won't you address the fact you won't use the formal construction?
Tim Golden BandTech.com
2020-10-21 14:15:05 UTC
Post by Lalo T.
reciprocal of z₁
This z3 factor is really profound. I would never have guessed that such a neutral could be so useful. Yet there it is rounding out the values; netting symmetry in triplicate.

This could be a pretty big deal to those who are able to traverse this ground. Whereas we can claim the equivalence between the complex numbers and P3 this cubic(meaning triple; terrible terminology by the way due to the reference to rectilinear process within a nonorthogonal system) seems counter to the ordinary complex conjugate. Also there is a bit of semblance to the distance function.

There is room for a bigger surprise factor really up in P4 since there will be exceptional values. Yet the greatest surprise would be if the form stated more clearly how the exceptions work. Division by +1#1 will be impossible... or will it? What if the other option... the option to yield the entire ring (and by ring I mean the geometry of the complex plane)... this then will drive my complaint about the field requirement and would upset mathematics even more deeply.

This is to say that there is an alternative interpretation on the division by zero: it is possible to claim that any value is legitimate, and this is exactly what we witness when we actually do the reverse operation:
(1.23)(0) = 0 : any value will do
1.23 / 0 = x : any value will do
errr... that isn't quite convincing, but I'll stand by the interpretation. That division is merely a reverse operator; that the multiplication by zero performs a dimensional collapse; that its reverse operator thus performs a dimensional construction; this would mean that it is possible that the P4 division by zero may not generate any exceptions... this does not help develop the reciprocal and yet the possibility that the reciprocal could be profound is present. Interdimensional analysis tells me this. You've had a bit of time and you've been saying it too... hmmm... this is fun.

Alright, I am only beginning to see your argument on the uniquity of P2 to the reals. And I will have to stand by my same mantra, but this then should cause you to yield your interpretation. The first concession that I can see is actually within the code of polysign. I do use two values to code P2, and any systematic approach will need n magnitudinal values to process Pn. Still, there is a reduced form, and in that form we see exact correspondence to the reals. The possibility that there is some utility in carrying around large numbers in balanced form could possibly be meaningful. The geometry is still local.

In effect going here topples more of mathematics, for it claims that what we think of as one dimensional is actually two dimensional. Now I do have to misuse this word 'dimension' here, for we also have P1 whose peculiar behavior somehow still matches the terminology... though within this new interdimensional puzzle there is room for interpretation.

Going here opens up another system really where the ray is fundamental and we simply construct by unfolding rays. In their unbalanced form two rays do in fact construct a plane, but it is a plane with two edges. It is enough space to work in no different than all the work that we've ever done thus far actually has four edges as in the edges of a piece of paper. These nonorthogonal systems work in any angle, but when the angle achieves balance we witness the polysign form... and the dimension collapses.

Strict is polysign. Plenty strict. Plenty dimensional too. Kaleidoscopic to work in. The P4 reciprocal should have 256 terms; maybe more. Great work Lalo. I'm rooting for you.
So have you worked out P4 yet? No doubt you are working on it. It is possible I suppose that the complexity does go up, but I hope not.
Post by Lalo T.
(z₁)(z₂)(z₃) = *70
(z₁)(w) = *⁷/₇ = *1
I do not know which form would be, keep it as reciprocal of a sum, or,
send the information to the length-component.
zelos...@gmail.com
2020-10-22 05:17:09 UTC
Post by Tim Golden BandTech.com
Post by Lalo T.
reciprocal of z₁
This z3 factor is really profound. I would never have guessed that such a neutral could be so useful. Yet there it is rounding out the values; netting symmetry in triplicate.
This could be a pretty big deal to those who are able to traverse this ground. Whereas we can claim the equivalence between the complex numbers and P3 this cubic(meaning triple; terrible terminology by the way due to the reference to rectilinear process within a nonorthogonal system) seems counter to the ordinary complex conjugate. Also there is a bit of semblance to the distance function.
There is room for a bigger surprise factor really up in P4 since there will be exceptional values. Yet the greatest surprise would be if the form stated more clearly how the exceptions work. Division by +1#1 will be impossible... or will it? What if the other option... the option to yield the entire ring (and by ring I mean the geometry of the complex plane)... this then will drive my complaint about the field requirement and would upset mathematics even more deeply.
(1.23)(0) = 0 : any value will do
1.23 / 0 = x : any value will do
errr... that isn't quite convincing, but I'll stand by the interpretation. That division is merely a reverse operator; that the multiplication by zero performs a dimensional collapse; that its reverse operator thus performs a dimensional construction; this would mean that it is possible that the P4 division by zero may not generate any exceptions... this does not help develop the reciprocal and yet the possibility that the reciprocal could be profound is present. Interdimensional analysis tells me this. You've had a bit of time and you've been saying it too... hmmm... this is fun.
Alright, I am only beginning to see your argument on the uniquity of P2 to the reals. And I will have to stand by my same mantra, but this then should cause you to yield your interpretation. The first concession that I can see is actually within the code of polysign. I do use two values to code P2, and any systematic approach will need n magnitudinal values to process Pn. Still, there is a reduced form, and in that form we see exact correspondence to the reals. The possibility that there is some utility in carrying around large numbers in balanced form could possibly be meaningful. The geometry is still local.
In effect going here topples more of mathematics, for it claims that what we think of as one dimensional is actually two dimensional. Now I do have to misuse this word 'dimension' here, for we also have P1 whose peculiar behavior somehow still matches the terminology... though within this new interdimensional puzzle there is room for interpretation.
Going here opens up another system really where the ray is fundamental and we simply construct by unfolding rays. In their unbalanced form two rays do in fact construct a plane, but it is a plane with two edges. It is enough space to work in no different than all the work that we've ever done thus far actually has four edges as in the edges of a piece of paper. These nonorthogonal systems work in any angle, but when the angle achieves balance we witness the polysign form... and the dimension collapses.
Strict is polysign. Plenty strict. Plenty dimensional too. Kaleidoscopic to work in. The P4 reciprocal should have 256 terms; maybe more. Great work Lalo. I'm rooting for you.
So have you worked out P4 yet? No doubt you are working on it. It is possible I suppose that the complexity does go up, but I hope not.
Post by Lalo T.
(z₁)(z₂)(z₃) = *70
(z₁)(w) = *⁷/₇ = *1
I do not know which form would be, keep it as reciprocal of a sum, or,
send the information to the length-component.
Why won't you use the formal construction?
Lalo T.
2020-10-22 07:49:15 UTC
If you want to check the reciprocal for polysigned p5 number
(or at least, to check the viability of the method), you could write a
simple program (if you really want to)

(well, reciprocal as general as possible, due to annihilators !!)

Alternatively, use symbol "&" for the fifth sign for the last p5 sign, and,
although the symbol "&" is, in several font styles, accomplished in just one stroke.
https://en.wikipedia.org/wiki/Ampersand#/media/File:Ampersand.svg
https://en.wikipedia.org/wiki/Ampersand
you can take out the selfintersections points of the symbol, to get five strokes
& - ⏧⏧ = |||||

z₁ = -a @ +b @ *c @ #d @ &e

( &1 / z₁ ) = ( &1 / (-a @ +b @ *c @ #d @ &e) ) = ??

z1 = -a @ +b @ *c @ #d @ &e
z₂ = +a @ #b @ -c @ *d @ &e
z₃ = *a @ -b @ #c @ +d @ &e
z₄ = #a @ *b @ +c @ -d @ &e
z₅ = &a @ &b @ &c @ &d @ &e

Undoubtedly, it would require be more careful, but temporally you could :

( &1 / z₁ ) = ( &1·z₂·z₃·z₄·z₅ / z₁·z₂·z₃·z₄·z₅ ) = ??

5^5 = 3125 terms

If you look the denominator for the p3 case

z₁·z₂·z₃ = *a³ @ *b³ @ *c³ @ -3abc @ +3abc

you may apply a "negation" operator to compact the number of terms

z₁·z₂·z₃ = *a³ @ *b³ @ *c³ @ negation(*3abc)
z₁·z₂·z₃ = *a³ @ *b³ @ *c³ @ ∾(*3abc)

where you can observe that there are terms "only" with the '*' symbol and
terms with the negation of '*' symbol.

If, for the denominator in the case of polysign p5 numbers,there were only terms
with the sign '&' and terms with the negation of '&', one could be talking of
some kind of reciprocal. The fact that 3000 terms get canceled or not,
is not so important.

In any case, with a program, it could be checked before breakfast time...
Tim Golden BandTech.com
2020-10-23 15:56:14 UTC
Fri 23 Oct 2020 10:08:51 AM EDT
Post by Lalo T.
If you want to check the reciprocal for polysigned p5 number
(or at least, to check the viability of the method), you could write a
simple program (if you really want to)
(well, reciprocal as general as possible, due to annihilators !!)
Alternatively, use symbol "&" for the fifth sign for the last p5 sign, and,
although the symbol "&" is, in several font styles, accomplished in just one stroke.
https://en.wikipedia.org/wiki/Ampersand#/media/File:Ampersand.svg
https://en.wikipedia.org/wiki/Ampersand
you can take out the selfintersections points of the symbol, to get five strokes
& - ⏧⏧ = |||||
There is no need to push for a fifth ASCII sign. In truth you could drop your @ notation and just allow the zero sign to take the fifth sign, which is equivalent notation. Next on then to a sixth sign? We could, but ordered series notation is available and it is the most reasonable thing to do in high sign. Rewriting to my usual notation
z₁ = - a + b * c # d @ e
and there is no conflict is there? I'm not bitching about your notation; rather I am willing to flex with it though this form is simpler. Here at P5; well; if you insist that the zero sign must have a corresponing upper sign then we'd top out at P4 notation and have to move over to ordered series here in P5. Also you have some characters after your ampersand:
& - ⏧⏧ = |||||
Post by Lalo T.
( &1 / z₁ ) = ( &1·z₂·z₃·z₄·z₅ / z₁·z₂·z₃·z₄·z₅ ) = ??
5^5 = 3125 terms
If you look the denominator for the p3 case
you may apply a "negation" operator to compact the number of terms
where you can observe that there are terms "only" with the '*' symbol and
terms with the negation of '*' symbol.
Yes, and further in reduced form the inverse term goes away because one of the components will be zero. The polysign balanced system is intact within your method. To round this out though could we ever achieve an inverse value? I don't think so and yet I don't have the proof either. It is a very generic sort of puzzle and I wouldn't doubt if somebody worked it out but I don't know who. This is right close by to the puzzle of freedom in P4 on
( - a + b )( + c # d ).
Though they are signed puzzles the sign sort of goes away in the puzzle.
This is what I love about the neutral term in the reciprocal. Who would ever guess that multiplying by
( * a * b * c ) (P3)
could be functional? I wouldn't. Obviously you did or you've come up with some numerical analysis that does. I may have discovered polysign but I'm prepared to pass the torch here. I don't know if I will be able even to keep up with this work. It is a wonderful opening into number theory isn't it? And the numbers are so simple.
Post by Lalo T.
If, for the denominator in the case of polysign p5 numbers,there were only terms
with the sign '&' and terms with the negation of '&', one could be talking of
some kind of reciprocal. The fact that 3000 terms get canceled or not,
is not so important.
In any case, with a program, it could be checked before breakfast time...
Yes, and here I am caught eating my thread for lunch because the program which will check this will be polynomial driven. Well, this is as it should be. The ambiguity is still present as with many other ambiguities in mathematics.
Anyway we are well within the finite domain here but I see you don't really want to give away your method just yet do you? It's fun. So how about P4?

z1 = - a + b * c # d
z2 = + a # b + c # d
z3 = * a + b - c # d
z4 = # a # b # c # d

I am still tempted to put the # component in another place for z2 so I'll have to admit that I'm still not seeing it. It is neat to see that a puzzle of four signs becomes a puzzle of three signs; but I really am just monkeying around. I have no idea if that is correct or not. Alright I've done a simple trace and gotten it backwards off of P5. 256 terms. I'm not saying its right. But I'm prepared to check it... once I get my gumption going. And I still don't see why. Great stuff Lalo.

P5 :
z1 = - a + b * c # d @ e
z₂ = + a # b - c * d @ e
z₃ = * a - b # c + d @ e
z₄ = # a * b + c - d @ e
z₅ = @ a @ b @ c @ d @ e
Lalo T.
2020-10-24 00:12:06 UTC
Maybe there are much more better symbol compared with the symbol '&'.

< I may have discovered polysign but I'm prepared to pass the torch here

Giving up something in what you have put a big amount of energy that easy ?

< It is a wonderful opening into number theory isn't it?

well, it could be added that the product rule does not have to be necessarily tied
to "cyclic stuff", or latin squares, but, undoubtedly, it is more attractive.
https://en.wikipedia.org/wiki/Latin_square

< which do not map here on my computer.

https://en.wikipedia.org/wiki/Miscellaneous_Technical#/media/File:U+23E7.svg

< I am still tempted to put the # component in another place

( &1 / z₁ ) = ( &1·G·H·K / z₁·G·H·K )

G = - 2a # 2b * 6c + 3d @ 9e
well, you could put an arbitrary G, H, K etc
It is like root rationalisation, but "sign rationalization"

Suppose that in the denominator you have something, and

*1/(something)

...multiplying

(*1·H) / (something·H)

...you get

( *1 / (-a @ +b @ *b) )

( *1 / (-a @ negation(-b)) )
when a > b

< ( * a * b * c ) (P3)
mmm, now that you mention, it is not essential multiplying by ( * a * b * c ) !!
But, if you don use it the denominator would have more terms, although the max
degree of the terms will be n-1

p4 is not a prime number, hence, a bit more "bad-tempered". The product rule
is "mod 4"...

< ...cancelling bunch so for instance the abccd components

-abccd @ +abccd @ *abccd @ #abccd @ @abccd = 0
Tim Golden BandTech.com
2020-10-24 16:05:47 UTC
Post by Lalo T.
Maybe there are much more better symbol compared with the symbol '&'.
< I may have discovered polysign but I'm prepared to pass the torch here
Giving up something in what you have put a big amount of energy that easy ?
No I'll never give up, but you deserve huge recognition. The energy you are spending on exhaustive background research I could never manage. And so far I don't think I'd ever discover this reciprocal either. Hopefully I'll get to a point where I can wrap my head around it, but Like Newton's gravitational theory: it only gets to be discovered once Lalo.

I did post a guess at the P4 reciprocal, but google is now truncating text so you have to click on the blue text at the bottom of posts here at the moment.

Still haven't gotten up the gumption on proving it but it should be quite doable using the text editor as I did for P3. A lot more cancellations... I have sage running here but I'm nowhere near to knowing how to enter these into it...
sage: 5^5
3125
sage: 4^4
256
sage: 5!
File "<ipython-input-6-8de0a076b17c>", line 1
Integer(5)!
^
SyntaxError: invalid syntax

sage: help(factorial)

sage: factorial(5)
120
sage: 120/5
24
sage: 0.5^3
0.125000000000000
sage: 4^4
256
Post by Lalo T.
< It is a wonderful opening into number theory isn't it?
well, it could be added that the product rule does not have to be necessarily tied
to "cyclic stuff", or latin squares, but, undoubtedly, it is more attractive.
https://en.wikipedia.org/wiki/Latin_square
I see the 'orthogonal representation' has some similarity, but I don't really see distribution in the puzzle. I'm thinking there is an argument out of pure symmetry that will do.
Post by Lalo T.
< which do not map here on my computer.
https://en.wikipedia.org/wiki/Miscellaneous_Technical#/media/File:U+23E7.svg
< I am still tempted to put the # component in another place
( &1 / z₁ ) = ( &1·G·H·K / z₁·G·H·K )
well, you could put an arbitrary G, H, K etc
It is like root rationalisation, but "sign rationalization"
Suppose that in the denominator you have something, and
*1/(something)
...multiplying
(*1·H) / (something·H)
...you get
when a > b
< ( * a * b * c ) (P3)
mmm, now that you mention, it is not essential multiplying by ( * a * b * c ) !!
But, if you don use it the denominator would have more terms, although the max
degree of the terms will be n-1
Seems to work very nicely with it. In terms of dealing in concrete values it clearly does not do much, but in terms of the proof it is enforcing symmetry. It's got to be there to get your cubic terms in P3. It is the most peculiar of the bunch. Very excellent. Fascinating. Subtle. Neutral. Really it has to be there to develop the cancellations too doesn't it? It's like it fills out the thing. It's bringing symmetry to the quantities without upsetting the sign mechanics.
Post by Lalo T.
p4 is not a prime number, hence, a bit more "bad-tempered". The product rule
is "mod 4"...
< ...cancelling bunch so for instance the abccd components
Yes for P5, and further though there are 24 groups of them. Makes me chuckle.
Really this whole thing is very open and maybe there is a grand short cut. I'm enjoying the cryptic dismantling of the thing here. Take your time as you like.
Lalo T.
2020-10-25 08:45:31 UTC
z1 = -3 @ +5 @ *11 @ #17 @ &29 = -3 @ +5 @ *11 @ #17 @ @29

w = -(53861/250480) @ +(54845/250480) @ *(53789/250480) @ #(48813/250480) @ &(63317/250480)

z1·w = -(3520029/250480) @ +(3520029/250480) @ *(3520029/250480) @ #(3520029/250480) @ &(3770509/250480)

z1·w = &(250480/250480) = @(250480/250480) = &1 = @1

The above example was done just numerically, but it has trick.
In anycase, was done under the following observation :

(@1 / z1) = ( (@1·z2·z3·z4) / (z1·z2·z3·z4) )

in this way, z5 ( only with terms with sign @) was excluded.

and optionally, associating (while operating)

((z1·z4)·(z2·z3)) <---

more or less, in the same way compared to polysign p3

yes, the number of terms grow quickly...
Lalo T.
2020-10-26 04:38:06 UTC
Did Descartes refer in his work only to operations addition and subtraction ?
Tim Golden BandTech.com
2020-10-28 17:35:36 UTC
Wed 28 Oct 2020 11:52:52 AM EDT
Post by Lalo T.
Did Descartes refer in his work only to operations addition and subtraction ?
No: he was all about multiplication and division and provided a graphical interpretation in Rules for the Direction of the Mind. However I believe that moderns will quibble over that interpretation and further had he filled it out more he would arrive at some conundrums. Well: his book ends in incompletion right around this place. His Rule XX (Rule 20):
"When we have found our equations, we must complete the operations which we have omitted, never using multiplication when there is opportunity for division."
was never filled out with any text. I suspect he was not happy with his interpretation. The initial concept was three books; each with twelve rules; all perfect. Maybe he just went on to better bigger things.In La Geometrie he manages to bump into imaginary roots while still thinking in terms of magnitude. His magnitude does have subtraction but he does not arrive with negative numbers easily. Nowhere in his primitive writings that I can name at this moment does he show a real line with positive and negative values. Here to double check myself I go to the table of contents but I see only

RULES FOR THE DIRECTION OF THE MIND
BOOK ONE
RULE I ................................... 3
RULE II ................................... 5
RULE III ................................... 8
RULE IV ................................... 12
...
RULE XII ................................... 12
BOOK TWO
RULE I ................................... 3
RULE II ................................... 5
RULE III ................................... 8
RULE IV ................................... 12
...
RULE XXI ................................... 92

and doing a brief scan of the book I can say that there is no real line there though there are many a segment; a square; a rectangle; and no formal Euclidean geometry. This is Rene's primitive source. The first book is really a philosophy that includes a few rudiments of mathematics such as enumeration (taken as granted), but really he is right up to dimensional analysis from the get-go and right down to the point...
" by a point, . , if we consider nothing else bit that it is a to form part of a quantity. But whatever way it is depicted and conceived, we always understand that it is an object extended in every way and capable of an infinity of dimensions. In the same way, also, we exhibit the terms of a problem to our eyes, if we are to pay attention to two of their different magnitudes sumultaneously, by the rectangle, two sides of which are the two magnitudes under consideration: in this way should they be incommensurable..."

but this interesting part of the quote is in the context of a discussion on unity and its taking forms such as a square or segment or a point. This is the real object under discussion in this partial quote above.

That we now have division in Pn marks a stage for the native well being and development of polysign.
Lalo T.
2020-10-28 19:34:43 UTC
z1 = -a +b *c <==> (a,b,c)

z2 = -a @ +b @ *c @ 0 <=?=> (a,b,c) non-null a,b,c

What was the perception of Descartes in regards to zero '0' ?
Does he use null magnitutes/quantities ?
In which contexts he make use of zero ?
(and square roots ?)
does he use zero, but not in relation to the usage of an origin ?
< http://wiki.gis.com/wiki/index.php/Pointed_space
does he use zero as an 'distinguished element', as an 'aditive neutral element' ?
Did in his usage of variable meant unknown magnitude or non-null unknown magnitude ?
( never directed magnitudes ? )
What was the domain that descartes endow to parameters and variables ?

One may suppose that things could be a bit more clearing swiming a bit in
variation of coordinates systems :

https://en.wikipedia.org/wiki/Two-center_bipolar_coordinates
https://en.wikipedia.org/wiki/Biangular_coordinates
https://en.wikipedia.org/wiki/Bipolar_coordinates

< but this interesting part of the quote is in the context of a discussion on unity and its taking forms such as a square or segment or a poin
you could expand on this poiint..

< That we now have division in Pn marks a stage for the native well being and development of polysign.
well, number-wise or term-wise, but, you also could send the 'division info' exclusively to the length component and keeping only product at term level

" Descartes himself used the transformation x → –x for using his rule for
getting information of the number of negative roots. " ??
https://en.wikipedia.org/wiki/Descartes%27_rule_of_signs ??

https://en.wikipedia.org/wiki/Quartic_function#Descartes'_solution ??
https://en.wikipedia.org/wiki/Descartes%27_theorem ??
https://en.wikipedia.org/wiki/Fermat_cubic ??
https://en.wikipedia.org/wiki/Folium_of_Descartes ??

https://en.wikipedia.org/wiki/Y-intercept

... available web articles about Descartes are imbued by modern perception...
Lalo T.
2020-10-28 20:27:21 UTC
< His magnitude does have subtraction but he does not arrive with negative
< numbers easily. Nowhere in his primitive writings that I can name at this
< moment does he show a real line with positive and negative values "

although different from the Number Line, possibly different to
min( |~a| , 0 ) = |~a|

and, also different to
min( ~a , +a ) = ~a ?

did he assign some properties to 'negative numbers' ?
what he meant by the algebra/arithmetic of negative numbers ?
Tim Golden BandTech.com
2020-10-29 13:01:56 UTC
Thu 29 Oct 2020 08:37:58 AM EDT
Post by Lalo T.
< His magnitude does have subtraction but he does not arrive with negative
< numbers easily. Nowhere in his primitive writings that I can name at this
< moment does he show a real line with positive and negative values "
although different from the Number Line, possibly different to
min( |~a| , 0 ) = |~a|
and, also different to
min( ~a , +a ) = ~a ?
did he assign some properties to 'negative numbers' ?
what he meant by the algebra/arithmetic of negative numbers ?
Dover Books ISBN 0-486-60068-8 Renes Descartes La Geometrie(1637) tranlated by David Eugene Smith and Marcia L. Latham (1925)

Book III
ON THE CONSTRUCTION OF SOLID OR SUPERSOLID PROBLEMS
What are false roots............ 372
"Every equation can have as many distinct roots (values of the unknown quantity) as the number of dimensions of the unknown quantity in the equation. Suppose, for example, x=2 or x-2=0, and again, x=3, or x-3=0. Multiplying together the two equations x-2=0 and x-3=0, we have xx-5x+6=0, or xx=5x-6. This is an equation in which x has the value 2 and at the same time x has the value 3. If we next make x-4=0 and multiply this by xx-5x+6=0 we have xxx-9xx+26x-24=0 another equation, in which x, having three dimensions, has also three values, namely, 2, 3, and 4.
It often happens, however, that some of the roots are false or less than nothing. Thus, if we suppose x to represent the defect of a quantity 5, we have x+5=0 which, multiplied by xxx-9xx+26x-24=0 yields xxxx-4xxx-19xx+106x-120=0, an equation having three true roots 2, 3, 4, and one false root, 5."

He then goes on to state the alternate sign rule which allows the flipping of true and false roots.

It seems to me that he is comfortable with an x=0 situation, but never will x be negative. The sense of magnitude as natural and unsigned is very present in his thinking.
zelos...@gmail.com
2020-10-30 06:32:49 UTC
Post by Tim Golden BandTech.com
Thu 29 Oct 2020 08:37:58 AM EDT
Post by Lalo T.
< His magnitude does have subtraction but he does not arrive with negative
< numbers easily. Nowhere in his primitive writings that I can name at this
< moment does he show a real line with positive and negative values "
although different from the Number Line, possibly different to
min( |~a| , 0 ) = |~a|
and, also different to
min( ~a , +a ) = ~a ?
did he assign some properties to 'negative numbers' ?
what he meant by the algebra/arithmetic of negative numbers ?
Dover Books ISBN 0-486-60068-8 Renes Descartes La Geometrie(1637) tranlated by David Eugene Smith and Marcia L. Latham (1925)
Book III
ON THE CONSTRUCTION OF SOLID OR SUPERSOLID PROBLEMS
What are false roots............ 372
"Every equation can have as many distinct roots (values of the unknown quantity) as the number of dimensions of the unknown quantity in the equation. Suppose, for example, x=2 or x-2=0, and again, x=3, or x-3=0. Multiplying together the two equations x-2=0 and x-3=0, we have xx-5x+6=0, or xx=5x-6. This is an equation in which x has the value 2 and at the same time x has the value 3. If we next make x-4=0 and multiply this by xx-5x+6=0 we have xxx-9xx+26x-24=0 another equation, in which x, having three dimensions, has also three values, namely, 2, 3, and 4.
It often happens, however, that some of the roots are false or less than nothing. Thus, if we suppose x to represent the defect of a quantity 5, we have x+5=0 which, multiplied by xxx-9xx+26x-24=0 yields xxxx-4xxx-19xx+106x-120=0, an equation having three true roots 2, 3, 4, and one false root, 5."
He then goes on to state the alternate sign rule which allows the flipping of true and false roots.
It seems to me that he is comfortable with an x=0 situation, but never will x be negative. The sense of magnitude as natural and unsigned is very present in his thinking.
Tim Golden BandTech.com
2020-10-28 14:27:38 UTC
Post by Lalo T.
The above example was done just numerically, but it has trick.
and optionally, associating (while operating)
((z1·z4)·(z2·z3)) <---
more or less, in the same way compared to polysign p3
yes, the number of terms grow quickly...
Well this P5 instance means a lot. No hidden dimensional quagmire.
I think it is going to work in P4 too.
The basic algorithm as I see it is to increment the signs by 1, 2, 3, and so on in each column. Possibly the ordered series helps expose this, but it has to come with the recognition of the wraparound in a finite sign system. Using
( 1, 0, 0, 0 ... )( 1, 0, 0, 0 ... ) = (1, 0, 0, 0 ... )
notation (the identity sign occupies the first position and minus the second position and so on)
In Pn:
z1 = ( x0, x1, x2, x3, ... x(n-1))
z2 = (x0, 0, x1, 0, x2, 0, x3, 0, ... x(n-1))
z3 = ( x0, 0, 0, x1, 0, 0, x2, 0, 0, x3, 0, 0, ... x(n-1))
z4 = ( x0, 0, 0, 0, x1, 0, 0, 0, x2, 0, 0, 0, x3, 0, 0, 0, ... x(n-1))
...

so for instance in a P3 signature we would stop at z3, which will translate to:
z3 = @ x0 @ x1 @ x2
and of course in the P4 system we would see that z4 would do likewise. Again back in P3 though we see that
z2 = @ x0 + x1 - x2
and
z1 = @ x0 - x1 + x2

Possibly the pure mathematician's proof is near in this format. By distributing out the modulo signs into the long series there will be room for the terms and their organization is more natural.
Pn; z1z2 = ( x0x0, x1x0 , x2x0, x3x0, ... x0x(n-1) )
@ ( 0, 0, x1x0, 0, x2x0, 0, x3x0, 0, ... x1x(n-1) )
@ ( 0, 0, 0, 0, x2x0, 0, x2x1, 0, x2x2, 0, x2x3, 0, ... x2x(n-1) )

this part will have to be done in a fixed width font which I am not trusting this google page to be. Anyway it looks as though diagonals of the same term are going to build up. The diagonals will come in shallow angles as well. I am not certain that this would actually become a full proof. It could be there will be need of some indirect means to organize it. Anyway the algorithm looks pretty good for Pn. My code already does the modulo math within the x[] array indexing so that in P3 x[5] is x[2] and so forth. I just have to dig in and implement this for the team. But we still have the puzzle of the zero divisors. Will the denominator come out to be zero in some cases and thus division by zero will prevent the reciprocal? I suppose this will have to be the case. I'd love for it to come out differently but I can't make that happen...

In the realm of dimensional analysis an option exists under such a division by zero. It can be viewed as a generator of an entire space filled with that goodness of infinity up a dimension. The other answer is anything. The question is anything where?
zelos...@gmail.com
2020-10-29 06:54:16 UTC
Post by Tim Golden BandTech.com
Post by Lalo T.
The above example was done just numerically, but it has trick.
and optionally, associating (while operating)
((z1·z4)·(z2·z3)) <---
more or less, in the same way compared to polysign p3
yes, the number of terms grow quickly...
Well this P5 instance means a lot. No hidden dimensional quagmire.
I think it is going to work in P4 too.
The basic algorithm as I see it is to increment the signs by 1, 2, 3, and so on in each column. Possibly the ordered series helps expose this, but it has to come with the recognition of the wraparound in a finite sign system. Using
( 1, 0, 0, 0 ... )( 1, 0, 0, 0 ... ) = (1, 0, 0, 0 ... )
notation (the identity sign occupies the first position and minus the second position and so on)
z1 = ( x0, x1, x2, x3, ... x(n-1))
z2 = (x0, 0, x1, 0, x2, 0, x3, 0, ... x(n-1))
z3 = ( x0, 0, 0, x1, 0, 0, x2, 0, 0, x3, 0, 0, ... x(n-1))
z4 = ( x0, 0, 0, 0, x1, 0, 0, 0, x2, 0, 0, 0, x3, 0, 0, 0, ... x(n-1))
...
and of course in the P4 system we would see that z4 would do likewise. Again back in P3 though we see that
and
Possibly the pure mathematician's proof is near in this format. By distributing out the modulo signs into the long series there will be room for the terms and their organization is more natural.
Pn; z1z2 = ( x0x0, x1x0 , x2x0, x3x0, ... x0x(n-1) )
@ ( 0, 0, x1x0, 0, x2x0, 0, x3x0, 0, ... x1x(n-1) )
@ ( 0, 0, 0, 0, x2x0, 0, x2x1, 0, x2x2, 0, x2x3, 0, ... x2x(n-1) )
this part will have to be done in a fixed width font which I am not trusting this google page to be. Anyway it looks as though diagonals of the same term are going to build up. The diagonals will come in shallow angles as well. I am not certain that this would actually become a full proof. It could be there will be need of some indirect means to organize it. Anyway the algorithm looks pretty good for Pn. My code already does the modulo math within the x[] array indexing so that in P3 x[5] is x[2] and so forth. I just have to dig in and implement this for the team. But we still have the puzzle of the zero divisors. Will the denominator come out to be zero in some cases and thus division by zero will prevent the reciprocal? I suppose this will have to be the case. I'd love for it to come out differently but I can't make that happen...
In the realm of dimensional analysis an option exists under such a division by zero. It can be viewed as a generator of an entire space filled with that goodness of infinity up a dimension. The other answer is anything. The question is anything where?
Lalo T.
2020-10-29 07:13:56 UTC
http://polysign.org/PolySigned/Lattice/Lattice.html

Alternatively, you could research if the paths/loops can be done
using the structural elements of the octahedron and tetrahedron (hybrid path),
not only between the origin and the structural elements of the
rhombic dodecahedron.

https://en.wikipedia.org/wiki/Rhombic_dodecahedral_honeycomb
https://en.wikipedia.org/wiki/Trigonal_trapezohedral_honeycomb
https://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycomb

https://mathworld.wolfram.com/SemiregularTessellation.html
https://en.wikipedia.org/wiki/Semiregular_polytope#Euclidean_honeycombs
Tim Golden BandTech.com
2020-10-29 16:40:34 UTC
Post by Lalo T.
http://polysign.org/PolySigned/Lattice/Lattice.html
Alternatively, you could research if the paths/loops can be done
using the structural elements of the octahedron and tetrahedron (hybrid path),
not only between the origin and the structural elements of the
rhombic dodecahedron.
One of the most excellent and interesting is not the regular but the irregular out of pure symmetry.
They are much like pi but there is more to them.
Take a simplex; select a face and reflect the simplex about that face. Easily done with the equilateral triangle to cover the plane with redundancy but the beauty is that it is a code that lays them out. A one of three selection in a long series. In 3D we have the tetrahedron and a one of four series elemental form. Just one vertex moves. People growing up with the turtle protocol game might readily understand them. The neatest thing then is to generate codes and see what comes out. Rings it turns out are extremely easy to code and the ends come out tantalizingly close to each other, yet we know there will always be some distance there. As you discuss loops these could as well be called solids. They are actually solids carrying correspondence with physical observation where it is admitted that while looking closely as matter it appears to be mostly empty space.
Somewhat string theory here but you see they bowed long ago to be some miniscule thing beneath the bigger physics. This theory would challenge atomic structure as we are taught it. It turns out to be that thermodynamic conduction actually requires such long distances to propagate. Oh my gosh. This is the truth. Lengthily coupled is loosely coupled. Then comes protein folding and these amazing nanomachines which keep us whirring all bathed in ATP syrup.

No this linkage is very loose still and will require quite some dimensional analysis to achieve locked states and HOH. Still by conservation of matter at the molecular level it will pass to choose a different dissection route so long as conservation is upheld. Of course then all the other correspondences would have to be upheld but getting the thermodynamics right is actually huge. How? Vibrating atoms as thermodynamics does not even pass the sniff test. Heat travels remarkably slowly through solids.

Possibly I am engaging here is some physics which takes the simplex route very seriously. In some ways the simplex chain is a proxy. All that really matters is correspondence. If we engage more structure in spacetime should we then see the complexity of the atom diminish? To deny the possibility would be foolish. To think so big as this; ummm, yeah; it is something I was taught to do I guess by my father at the dinner table. I am happy to set an example for others in the process of throwing open the doors, stepping down the stairs and getting our feet onto some soft ground. That concept is foreign to the city person, but here when you get off the trail in the woods the ground springs beneath you and it is the finest footing you could ask for.

These chains can also form segments when the code is right. Of course that segment structure is up a notch from the raw discrete geometry. It's pretty and its pure and it does carry enough congruence to bear study. Somebody will chime in with the 'oh that's a thus and such manifold with extensible limits' well fine then so what if it is? Constructive freedom works rather differently than a dictionary of terms; a rather lengthy and self referential dictionary at that; cross referenced into oblivion. These things have been done well before me but their common name is not with me. I wish the signon were so exciting, but it is just full lattice technology in a new format. It has a few oddities, but nothing like these chained simplices do. Maybe doing a code trace of a signon path tracking the chain... it's a data source if nothing else. It comes in different ranges.
The high res version should have quite a bit of redundancy. Just repetitive slope small step traces to the next vertex. Normally we'd do the math with double precision floats. Maybe this needs to be reconsidered. The rational meets the irrational here.
Post by Lalo T.
https://en.wikipedia.org/wiki/Rhombic_dodecahedral_honeycomb
https://en.wikipedia.org/wiki/Trigonal_trapezohedral_honeycomb
https://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycomb
https://mathworld.wolfram.com/SemiregularTessellation.html
https://en.wikipedia.org/wiki/Semiregular_polytope#Euclidean_honeycombs
Lalo T.
2020-10-29 22:15:13 UTC
< Book III
< ON THE CONSTRUCTION OF SOLID OR SUPERSOLID PROBLEMS
< What are false roots............ 372
< "Every equation can have as many distinct roots (values of the unknown
< quantity) as the number of dimensions of the unknown quantity in the equation.
< Suppose, for example, x=2 or x-2=0, and again, x=3, or x-3=0. Multiplying
< together the two equations x-2=0 and x-3=0, we have xx-5x+6=0, or xx=5x-6.
< This is an equation in which x has the value 2 and at the same time x has the
< value 3. If we next make x-4=0 and multiply this by xx-5x+6=0 we
< have xxx-9xx+26x-24=0 another equation, in which x, having three dimensions,
< has also three values, namely, 2, 3, and 4.
< It often happens, however, that some of the roots are false or less than
< nothing. Thus, if we suppose x to represent the defect of a quantity 5, we
< have x+5=0 which, multiplied by xxx-9xx+26x-24=0
< yields xxxx-4xxx-19xx+106x-120=0, an equation having three true
< roots 2, 3, 4, and one false root, 5."

I would have to examine it further, how he contain/isolate the arithmetic
of 'false roots'. Other way could be examining the Descartes correspondence
with other people, or mathematical literature about him
(single axis, curve contruction, the relationship of algebra and geometry, etc)
in order to have an idea of what he meant by managing false roots, different
than number line ? (it seems a rather long task...)

I wonder if exist more ways to get reciprocals.
It could take you explore more deeply the geometrical aspects to get your polysign
p4 reciprocal.
Or maybe finding some hidden additive properties/geometrical consideration
without involving product.

It sounds good Nature and springs :)

"Zero-sum permutation"
https://en.wikipedia.org/wiki/H4_polytope#Coordinates
"barycentric coordinates" "freely permuted"
Regular and Semi-Regular Polytopes II, Four-dimensional polytopes by H. Coxeter
https://en.wikipedia.org/wiki/Harold_Scott_MacDonald_Coxeter

Symmetry beyond groups by Rui Loja Fernandes
https://www.math.tecnico.ulisboa.pt/~rfern/Meus-papers/HTML/ISRLect.pdf

https://skeptics.stackexchange.com/questions/40022/did-ren%C3%A9-descartes-develop-the-cartesian-coordinate-system-by-watching-a-fly-on

The Correspondence of René Descartes 1643 edited by Theo Verbeek, Erik-Jan Bos, and Jeroen van de Ven
Rene Descartes Foundations of Analytic Geometry and Classification of Curves by Sofia Neovius
Descartes Philosophical Revolution: A Reassessment by Hanoch Ben-Yami
Historical Dictionary of Descartes and Cartesian Philosophy" by Roger Ariew, Dennis Des Chene, Douglas M. Jesseph, Tad M. Schmaltz, and Theo Verbeek
The Cambridge Descartes lexicon by Lawrence Nolan
Analysis, Synthesis, the Infinite, and Numbers by Steven Williams
A Source Book in Mathematics, 1200-1800, by Dirk Jan Struik
https://archive.org/details/B-001-001-112/page/n9/mode/2up
A History Of Mathematical Notations Vol I by Florian Cajori
https://archive.org/details/historyofmathema031756mbp
History of Analytic Geometry by Carl B. Boyer
Geometry by Its History by Alexander Ostermann and Gerhard Wanner

https://en.wikipedia.org/wiki/Grid_reference
https://en.wikipedia.org/wiki/Coordinate-free
https://en.wikipedia.org/wiki/Graph_of_a_function#Examples
https://mathworld.wolfram.com/CartesianCoordinates.html
https://hsm.stackexchange.com/questions/2372/is-it-true-that-leibniz-introduced-constant-variable-and-function
https://en.wikipedia.org/wiki/Coordinate_system#Coordinate_lines/curves_and_planes/surfaces
https://en.wikipedia.org/wiki/Curve#History
https://en.wikipedia.org/wiki/Gallery_of_curves
http://xahlee.info/surface/gallery.html
Tim Golden BandTech.com
2020-10-30 17:34:53 UTC
Post by Lalo T.
< Book III
< ON THE CONSTRUCTION OF SOLID OR SUPERSOLID PROBLEMS
< What are false roots............ 372
< "Every equation can have as many distinct roots (values of the unknown
< quantity) as the number of dimensions of the unknown quantity in the equation.
< Suppose, for example, x=2 or x-2=0, and again, x=3, or x-3=0. Multiplying
< together the two equations x-2=0 and x-3=0, we have xx-5x+6=0, or xx=5x-6.
< This is an equation in which x has the value 2 and at the same time x has the
< value 3. If we next make x-4=0 and multiply this by xx-5x+6=0 we
< have xxx-9xx+26x-24=0 another equation, in which x, having three dimensions,
< has also three values, namely, 2, 3, and 4.
< It often happens, however, that some of the roots are false or less than
< nothing. Thus, if we suppose x to represent the defect of a quantity 5, we
< have x+5=0 which, multiplied by xxx-9xx+26x-24=0
< yields xxxx-4xxx-19xx+106x-120=0, an equation having three true
< roots 2, 3, 4, and one false root, 5."
I would have to examine it further, how he contain/isolate the arithmetic
of 'false roots'. Other way could be examining the Descartes correspondence
with other people, or mathematical literature about him
(single axis, curve contruction, the relationship of algebra and geometry, etc)
in order to have an idea of what he meant by managing false roots, different
than number line ? (it seems a rather long task...)
I wonder if exist more ways to get reciprocals.
It could take you explore more deeply the geometrical aspects to get your polysign
p4 reciprocal.
Or maybe finding some hidden additive properties/geometrical consideration
without involving product.
It sounds good Nature and springs :)
"Zero-sum permutation"
https://en.wikipedia.org/wiki/H4_polytope#Coordinates
"barycentric coordinates" "freely permuted"
Regular and Semi-Regular Polytopes II, Four-dimensional polytopes by H. Coxeter
https://en.wikipedia.org/wiki/Harold_Scott_MacDonald_Coxeter
Symmetry beyond groups by Rui Loja Fernandes
https://www.math.tecnico.ulisboa.pt/~rfern/Meus-papers/HTML/ISRLect.pdf
https://skeptics.stackexchange.com/questions/40022/did-ren%C3%A9-descartes-develop-the-cartesian-coordinate-system-by-watching-a-fly-on
The Correspondence of René Descartes 1643 edited by Theo Verbeek, Erik-Jan Bos, and Jeroen van de Ven
Rene Descartes Foundations of Analytic Geometry and Classification of Curves by Sofia Neovius
Descartes Philosophical Revolution: A Reassessment by Hanoch Ben-Yami
Historical Dictionary of Descartes and Cartesian Philosophy" by Roger Ariew, Dennis Des Chene, Douglas M. Jesseph, Tad M. Schmaltz, and Theo Verbeek
The Cambridge Descartes lexicon by Lawrence Nolan
Analysis, Synthesis, the Infinite, and Numbers by Steven Williams
A Source Book in Mathematics, 1200-1800, by Dirk Jan Struik
https://archive.org/details/B-001-001-112/page/n9/mode/2up
A History Of Mathematical Notations Vol I by Florian Cajori
https://archive.org/details/historyofmathema031756mbp
History of Analytic Geometry by Carl B. Boyer
Geometry by Its History by Alexander Ostermann and Gerhard Wanner
https://en.wikipedia.org/wiki/Grid_reference
https://en.wikipedia.org/wiki/Coordinate-free
https://en.wikipedia.org/wiki/Graph_of_a_function#Examples
https://mathworld.wolfram.com/CartesianCoordinates.html
https://hsm.stackexchange.com/questions/2372/is-it-true-that-leibniz-introduced-constant-variable-and-function
https://en.wikipedia.org/wiki/Coordinate_system#Coordinate_lines/curves_and_planes/surfaces
https://en.wikipedia.org/wiki/Curve#History
https://en.wikipedia.org/wiki/Gallery_of_curves
http://xahlee.info/surface/gallery.html
Please tell me if you can see this graphic:
And also if this let's you see about six graphics at the moment:
I think it may be Coxeter did study them and he may have had a name for them too. I wish they were easier to research but as I got into them through my brother's beckoning we did find a few references in time but not much. That these discrete objects are developing nearly perfect circles has to be worthy of study. As to how these details connect to ordinary affairs... it seems a long way around.

At the time of Descartes writing La Geometrie he clearly was not having negative numbers. It is just as I have alluded to before: subtraction becomes a necessary operation to perform algebra and in doing so these possibilities arise. A negative resultant is not recognized as such. It does not exist and so is called 'false'. The formalization of the real number occurred later, and our usage of 'cartesian' coordinates is a misnomer. He has bumped into the cause for real numbers and possibly did consider the exception, much as P1 seems to demand exceptional mistreatment. He also manages to bump into imaginary roots without ever needing the real value. For Descartes the signs are operators; not values. There is no positive number; there is just number. Yet his number has far more life than today's digest allows for.
Lalo T.
2020-10-30 18:57:18 UTC
Maybe they didn t have negative or complex available, but they had ways of dealing with it, and
in the context of that time, it can be interesting to know what was going on in the 'collective mathematical mind'.

" He also inspired some of the innovations of Buckminster Fuller. "
in https://en.wikipedia.org/wiki/Harold_Scott_MacDonald_Coxeter

Yeah, I can visualize all. It seems like some structural thing in architecture, kind of some 'structural ring' in tensegrity.
maybe googling images or exploring https://tensegritywiki.com/wiki/Main_Page

Some ongoing research ? It looks good.
Lalo T.
2020-10-31 07:28:36 UTC
It would be cool some implementation using a newton-like method for reciprocal
just temporally, to get agood aprox(in case of be useful )

Fast inverse for big numbers: Picarte’s iteration
by Claudio Gutierrez and Mauricio Monsalve
https://www.dcc.uchile.cl/TR/2007/TR_DCC-2007-009.pdf

sign extension,zero extension
https://en.wikipedia.org/wiki/Sign_extension

prefix nearby numeral, but not prefix nearby variable

Maybe to model forces in a non-orthogonal approach.

I was not able to find specific literature. Optionally you could ask in
a math, in an architectural forum, structural engineering forum
in some Coxeter or conway literature..?

Maybe some resemblance (although not an exact match, referring to the approach)

https://en.wikipedia.org/wiki/Skew_polygon
https://en.wikipedia.org/wiki/Petrie_dual
https://en.wikipedia.org/wiki/Infinite_skew_polygon#Infinite_helical_polygons_in_three_dimensions <---
https://en.wikipedia.org/wiki/Infinite_skew_polygon
https://en.wikipedia.org/wiki/Skew_polygon

computing + nature = outdoor computing under the sun with sun readable screen OMG

what is the turtle protocol ?
Timothy Golden
2020-10-31 16:39:37 UTC
Post by Lalo T.
It would be cool some implementation using a newton-like method for reciprocal
just temporally, to get agood aprox(in case of be useful )
Fast inverse for big numbers: Picarte’s iteration
by Claudio Gutierrez and Mauricio Monsalve
https://www.dcc.uchile.cl/TR/2007/TR_DCC-2007-009.pdf
sign extension,zero extension
https://en.wikipedia.org/wiki/Sign_extension
prefix nearby numeral, but not prefix nearby variable
Maybe to model forces in a non-orthogonal approach.
I was not able to find specific literature. Optionally you could ask in
a math, in an architectural forum, structural engineering forum
in some Coxeter or conway literature..?
Maybe some resemblance (although not an exact match, referring to the approach)
https://en.wikipedia.org/wiki/Skew_polygon
https://en.wikipedia.org/wiki/Petrie_dual
https://en.wikipedia.org/wiki/Infinite_skew_polygon#Infinite_helical_polygons_in_three_dimensions <---
https://en.wikipedia.org/wiki/Infinite_skew_polygon
https://en.wikipedia.org/wiki/Skew_polygon
computing + nature = outdoor computing under the sun with sun readable screen OMG
what is the turtle protocol ?
https://en.wikipedia.org/wiki/Logo_(programming_language)
I'm actually working on path math for the moment. Calling them troll numbers but maybe Turtle numbers is more respectful. It is a basic truth that paths carry more physical correspondence than do the ordinary numerical forms. These happen to be string based and long values portray complexity. As to what and how much they can carry; this is a matter of constructive freedom. That their scalar nature already inhabit a sort of multiresolutional form... all that our math does is reduce them. Holding their form preserves their history. Their geometry is obvious and ordinary. Their trace is ray based. Their form stated most generally can take
Sigma ( s(n) x(n) )
where s is enumerated sign and x is continuous magnitude. But there is room for grammar atop this concept. This is just the MU^n form with a bit more freedom. You could say that the MU^n form is orderly and has no need of s(n) but that this form is disorderly and requires its enumerant. Their history can be compacted many ways. They have multiresolution. These are an obvious lead into calculus and hopefully of a new variety. If this theory holds up it could be that functional analysis will be challenged; dimantled; then recovered again as a rudimentary instance. This is the process of refactoring old systems. We've done in on the real number and it works. The prediction that this exists is obvious. How long it will take to get results is another thing.

One interesting detail on the Sigma(s(n)x(n)) system: it already is an ordered series. In other words the format
T4: + 2 - 3 + 1 * 5
is identically
T4: ( + 2, - 3, + 1, * 5 )
so in effect there is no need of any series representation. The sum is implied but is taken literally as a geometrical path. As such its preservation is of interest. Though the compacted form exists there do still exist unique geometric paths that can yield the same compacted form. Thus our operators as compactors versus as historical preservatives takes on meaning. T space in its raw form portrays jagged rays tracing out a path. These are unidirectional segments and obey the principles laid out in the polysign lattice, though they are of continuous form. The series representation only takes on value within each term. So for instance in large sign we might want
T4: ( 8, 2.01 ) @ ( 7, 1.3 ) @ ...
and so the earlier expression becomes
T4: ( 2, 2 ) @ ( 1, 3 ) @ ( 2, 1 ) @ ( 3, 5 )
but really these parentheses could be dropped I think. They are ( s, x ). We can drop the @'s and say
T4: ( 2, 2 ), ( 1, 3 ), ( 2, 1 ), ( 3, 5 )
but now I do see an ambiguity in the notation. Some future literalist will complain about the comma demarking two differing situations. Clarity is better with unique demarkation.
It is possible that two seemingly equivalent compacted t1, t2 have order.
For instance
t1 = - 1 + 2 * 3
t2 = + 2 * 3 - 1
have unique traces (renderings) though they are aligned at n=3. In truth there isn't even an origin yet. So much freedom here but I think the basic assumptions are still good. We can posit that
t1 < t2
so now we can order multidimensional things. It seems a bit of a cheat but it just happens to be the case. And these t need to be in the same system I would think, though they are very flexible and undemanding things. Enough for now. I don't mean to sidetrack us. Whatever. This thread becomes a manifesto I suppose. You've certainly have heaped a rather large series of links here so I can't feel too bad subjecting a reader to this meandering.

Peace Out Lalo!
Timothy Golden
2020-11-01 23:44:03 UTC
Post by Timothy Golden
Post by Lalo T.
It would be cool some implementation using a newton-like method for reciprocal
just temporally, to get agood aprox(in case of be useful )
Fast inverse for big numbers: Picarte’s iteration
by Claudio Gutierrez and Mauricio Monsalve
https://www.dcc.uchile.cl/TR/2007/TR_DCC-2007-009.pdf
sign extension,zero extension
https://en.wikipedia.org/wiki/Sign_extension
prefix nearby numeral, but not prefix nearby variable
Maybe to model forces in a non-orthogonal approach.
I was not able to find specific literature. Optionally you could ask in
a math, in an architectural forum, structural engineering forum
in some Coxeter or conway literature..?
Maybe some resemblance (although not an exact match, referring to the approach)
https://en.wikipedia.org/wiki/Skew_polygon
https://en.wikipedia.org/wiki/Petrie_dual
https://en.wikipedia.org/wiki/Infinite_skew_polygon#Infinite_helical_polygons_in_three_dimensions <---
https://en.wikipedia.org/wiki/Infinite_skew_polygon
https://en.wikipedia.org/wiki/Skew_polygon
computing + nature = outdoor computing under the sun with sun readable screen OMG
what is the turtle protocol ?
https://en.wikipedia.org/wiki/Logo_(programming_language)
I'm actually working on path math for the moment. Calling them troll numbers but maybe Turtle numbers is more respectful. It is a basic truth that paths carry more physical correspondence than do the ordinary numerical forms. These happen to be string based and long values portray complexity. As to what and how much they can carry; this is a matter of constructive freedom. That their scalar nature already inhabit a sort of multiresolutional form... all that our math does is reduce them. Holding their form preserves their history. Their geometry is obvious and ordinary. Their trace is ray based. Their form stated most generally can take
Sigma ( s(n) x(n) )
where s is enumerated sign and x is continuous magnitude. But there is room for grammar atop this concept. This is just the MU^n form with a bit more freedom. You could say that the MU^n form is orderly and has no need of s(n) but that this form is disorderly and requires its enumerant. Their history can be compacted many ways. They have multiresolution. These are an obvious lead into calculus and hopefully of a new variety. If this theory holds up it could be that functional analysis will be challenged; dimantled; then recovered again as a rudimentary instance. This is the process of refactoring old systems. We've done in on the real number and it works. The prediction that this exists is obvious. How long it will take to get results is another thing.
One interesting detail on the Sigma(s(n)x(n)) system: it already is an ordered series. In other words the format
T4: + 2 - 3 + 1 * 5
is identically
T4: ( + 2, - 3, + 1, * 5 )
so in effect there is no need of any series representation. The sum is implied but is taken literally as a geometrical path. As such its preservation is of interest. Though the compacted form exists there do still exist unique geometric paths that can yield the same compacted form. Thus our operators as compactors versus as historical preservatives takes on meaning. T space in its raw form portrays jagged rays tracing out a path. These are unidirectional segments and obey the principles laid out in the polysign lattice, though they are of continuous form. The series representation only takes on value within each term. So for instance in large sign we might want
and so the earlier expression becomes
T4: ( 2, 2 ), ( 1, 3 ), ( 2, 1 ), ( 3, 5 )
but now I do see an ambiguity in the notation. Some future literalist will complain about the comma demarking two differing situations. Clarity is better with unique demarkation.
It is possible that two seemingly equivalent compacted t1, t2 have order.
For instance
t1 = - 1 + 2 * 3
t2 = + 2 * 3 - 1
have unique traces (renderings) though they are aligned at n=3. In truth there isn't even an origin yet. So much freedom here but I think the basic assumptions are still good. We can posit that
t1 < t2
so now we can order multidimensional things. It seems a bit of a cheat but it just happens to be the case. And these t need to be in the same system I would think, though they are very flexible and undemanding things. Enough for now. I don't mean to sidetrack us. Whatever. This thread becomes a manifesto I suppose. You've certainly have heaped a rather large series of links here so I can't feel too bad subjecting a reader to this meandering.
Peace Out Lalo!
I think it can also be said that these are in fact polynomials. They are an extremely simple breed of polynomials.
We are actually free to define the sum and the product and would it be such a large conflict if the sum were the product?
t1 t2
speaks for itself really. They are appended. Their sum exists. Their product actually fits the freedoms of the rotational form that is already in use in the polynomial product of AA. Nothing extraordinary here. In fact extremely simplified over the old system. Physical correspondence too. There are many other operators to cover still, but they do this one thing very naturally and it happens to be the sum and the product as far as I can tell at the moment. I have to stress that these are graphical objects as much as they are numbers. I think of their geometry in polysign numbers but they may be transferable to other domains. At some level it really is just the logo language which I have yet to research. I've already seen everybody had a version including MIT. I think at the time the resolution of the hardware was poor. We used to dream what it would be like to have a 1Kx1K display. I remember hearing of logos and it sounded good. Chained simplices are way more fascinating. Mandelbrot and Julia too. Still in the mathematics we are at a primitive level and it is good to be primitive and stay primitive as long as there is ground to cover. Mow it. Dodge the rocks. Turn over the rocks. Dig them out. Pry them up. Primitive you see? Really wouldn't a drawing be nice. Primitive. Everything can be drawn. True/False; each way must be considered. Drawing; rendering; existing; it's a stretch yet all else is merely a portrayal of it. We seek out the smallest point and small have we gone. 1.616255(18)×10−35 m ; I don't know if I believe it.

Lalo that you discovered the reciprocal is such good news! I can't tell you how many times I look down your long lists of links worrying that I will miss something important if I don't cover them all and I do not cover them all. And sure enough I popped off onto here while really not digesting the fact that you already had this on 8/30/2020. I, enraged at your softness for AA, set out here to go over the ground again. And here we are now.
I think it is really great stuff, including the snivelling dweebs. Oh did you know we are having a presidential election in our country? I've been singing variations on a song now today and it is really sounding quite good:
"Fucking Fake America, Fucking Fake Again"
I used to just use the form
"Fake America Fake Again"
but the fucking in there really gives it rhythm. It is possible to transpose it to pretty much any format even a marching band style. You can just here the choir churning it out at the top of their lungs on a long march through town. This is how I identify with my country of origin now. I am ashamed to admit that I am an 'American' and who are the fatheads that took two continents of plurality for their own locality? And did what to them? Not just used and abused. No; starved and a few burned alive to provoke fear. This is my Cuntry.
Lalo T.
2020-11-02 05:18:16 UTC
as in that gif ?

< Oh did you know we are having a presidential election in our country?
I heard a bit on the topic. Some intense days...
Timothy Golden
2020-11-04 15:02:54 UTC
Post by Lalo T.
as in that gif ?
https://en.wikipedia.org/wiki/Turtle_graphics#/media/File:Turtle-animation.gif
< Oh did you know we are having a presidential election in our country?
I heard a bit on the topic. Some intense days...
Yeah, it really is just vector based graphics. Not dead and done at all. Today's svg is an instance of it in modern form. It begs for a protocol and then you get carried away making up your own variations and protocols. I had a vector based Tektronix oscilloscope and the graphics were great. Full text help screens. I guess if they wanted to go whole hog they could have drawn out the oscilloscope front panel on the screen. But that's thanks to a high grade phosphor coating and a well controlled electron beam. Now the GPUs are doing the work and we're in pixelated space from the get go. To study this technology at a mathematical level and even to wonder about the 'jagged' style... in linear systems those jags go away. The ultimate resolution of the vector based graphic is a matter of the thickness of the trace, and its longevity fits in nearby too. You can't just wipe the screen clear... though this could be an interesting branch of display technology. That we are struggling to make better light blocking devices says a lot. Anyway this is not gound breaking work. But it is fundamental work. To the modern mathematician the 'vector behaved' system is a strict requirement already built upon a cartesian style basis. At least I think this is the standard modern interpretation. We have successfully broken with orthogonality and find a new natural form though its angles are still quite strict.

What Descartes does and I feel forced to do as well as I inhabit polysign is interdimensional interpretation. And it is here that the product seems to deserve its place. In this way an attack on abstract algebra goes as a kick to one of the testes. There is so much room here to declare ambiguities that I fail to see how we can be claiming to be practicing mathematics. All the while abstract algebra is mum on any dimensional interpretation. It is deaf and mute in these terms.

Incidentally I have no children of my own though my testes do work; both of them.
zelos...@gmail.com
2020-11-05 06:31:11 UTC
Post by Lalo T.
as in that gif ?
https://en.wikipedia.org/wiki/Turtle_graphics#/media/File:Turtle-animation.gif
< Oh did you know we are having a presidential election in our country?
I heard a bit on the topic. Some intense days...
Yeah, it really is just vector based graphics. Not dead and done at all. Today's svg is an instance of it in modern form. It begs for a protocol and then you get carried away making up your own variations and protocols. I had a vector based Tektronix oscilloscope and the graphics were great. Full text help screens. I guess if they wanted to go whole hog they could have drawn out the oscilloscope front panel on the screen. But that's thanks to a high grade phosphor coating and a well controlled electron beam. Now the GPUs are doing the work and we're in pixelated space from the get go. To study this technology at a mathematical level and even to wonder about the 'jagged' style... in linear systems those jags go away. The ultimate resolution of the vector based graphic is a matter of the thickness of the trace, and its longevity fits in nearby too. You can't just wipe the screen clear... though this could be an interesting branch of display technology. That we are struggling to make better light blocking devices says a lot. Anyway this is not gound breaking work. But it is fundamental work. To the modern mathematician the 'vector behaved' system is a strict requirement already built upon a cartesian style basis. At least I think this is the standard modern interpretation. We have successfully broken with orthogonality and find a new natural form though its angles are still quite strict.
What Descartes does and I feel forced to do as well as I inhabit polysign is interdimensional interpretation. And it is here that the product seems to deserve its place. In this way an attack on abstract algebra goes as a kick to one of the testes. There is so much room here to declare ambiguities that I fail to see how we can be claiming to be practicing mathematics. All the while abstract algebra is mum on any dimensional interpretation. It is deaf and mute in these terms.
Incidentally I have no children of my own though my testes do work; both of them.
Why won't you answer my question?
Bassam Karzeddin
2020-10-31 07:32:25 UTC
Post by Lalo T.
Maybe they didn t have negative or complex available, but they had ways of dealing with it, and
in the context of that time, it can be interesting to know what was going on in the 'collective mathematical mind'.
" He also inspired some of the innovations of Buckminster Fuller. "
in https://en.wikipedia.org/wiki/Harold_Scott_MacDonald_Coxeter
Yeah, I can visualize all. It seems like some structural thing in architecture, kind of some 'structural ring' in tensegrity.
maybe googling images or exploring https://tensegritywiki.com/wiki/Main_Page
Some ongoing research ? It looks good.
The sci. math members have already and recently realized that the abstract algebra was broken a long time before abstract algebra itself started,

(when they did invent non-existing numbers like the cube root two since they have never well-understood the old ancient Greek problem about doubling the cube by any tools or any means (I only, added))

So to say, why to go the other much longer way to rebreak it again? Wonder!

Bassam Karzeddin
Lalo T.
2020-10-31 08:04:41 UTC
I dont know about the actual capacities of contemporary knowledge in "non-cyclical" oriented numeral systems.
There are some exotic numeral systems and string operations, like focusing in avoiding carry operation, maybe some other aspect.
...or in a tropical version of synthetic geometry, so to speak.
Timothy Golden
2020-10-31 15:10:33 UTC
Post by Lalo T.
I dont know about the actual capacities of contemporary knowledge in "non-cyclical" oriented numeral systems.
There are some exotic numeral systems and string operations, like focusing in avoiding carry operation, maybe some other aspect.
...or in a tropical version of synthetic geometry, so to speak.
You've certainly covered plenty already. At some point we simply identify the freedoms of construction. Some of them are quite hollow. Still others are possibly too concise. We exist in a reality that has tremendous redundancy. We witness the mistakes of our piers in the terms of dimension; a discrete quality of continuous extent. Such blasphemy is ruled by only one quality: correspondence. As one modern physicist goes astray on a fine tuned universe another exceeds all hope in a multiverse of every possibility playing itself out. The mathematician sits humbly by and confirms his divorce from physics.

I think most will confess that atomic theory is beyond them. Dig in though and you find the spectroscopic drive to atomic theory. Lots of n squares in there and so forth. The entire thing is curve fit work. There is nothing theoretical about the atomic structure. Particle/wave duality is the mathematicians problem as much as it is the physicists. Well what about that divorce? Divorce? What divorce? The mathematicians real number has been constructing modern physics all this time. They bow to the real value. Einstein certainly. Maxwell too. Should we break the real number then to what degree should all of that come under review?

Should unidirectional time gain a place in fundamental number theory and space its place right alongside in a structure that seems too good to be true to those who are used to pulling a three-eared rabbit out of their hat... I suppose we could put a rabbit with a spare and sharp ear under the bridge skulking around, maybe nibbling the top of a carrot... not stuck in the mud though. AA is my bitch now. The slitch that thinks she stole my heart. I'm taking it back. Their sum is not a sum. Their product not a product. Their X nothing at all. That is one X I won't be needing to file shit for... other than to run it under the bus.
Timothy Golden
2020-11-05 16:58:01 UTC
Post by Lalo T.
I dont know about the actual capacities of contemporary knowledge in "non-cyclical" oriented numeral systems.
There are some exotic numeral systems and string operations, like focusing in avoiding carry operation, maybe some other aspect.
...or in a tropical version of synthetic geometry, so to speak.
I think what we witness is that they in fact flourish. There are so many possible variations that we will be forced back to some basis. They are much like the string in computers; capable of supporting all sorts of types; the fundamental nature of the path does speak out loudly within the obnoxious realms of possibility. Getting up in dimension here seems to promise arbitrary branes. Getting down in dimension here seems to be Descarte's point.

Descarte's point was...
Descarte's point is...
Descarte's point will be...
zelos...@gmail.com
2020-11-02 06:29:42 UTC
Post by Tim Golden BandTech.com
Post by Lalo T.
< Book III
< ON THE CONSTRUCTION OF SOLID OR SUPERSOLID PROBLEMS
< What are false roots............ 372
< "Every equation can have as many distinct roots (values of the unknown
< quantity) as the number of dimensions of the unknown quantity in the equation.
< Suppose, for example, x=2 or x-2=0, and again, x=3, or x-3=0. Multiplying
< together the two equations x-2=0 and x-3=0, we have xx-5x+6=0, or xx=5x-6.
< This is an equation in which x has the value 2 and at the same time x has the
< value 3. If we next make x-4=0 and multiply this by xx-5x+6=0 we
< have xxx-9xx+26x-24=0 another equation, in which x, having three dimensions,
< has also three values, namely, 2, 3, and 4.
< It often happens, however, that some of the roots are false or less than
< nothing. Thus, if we suppose x to represent the defect of a quantity 5, we
< have x+5=0 which, multiplied by xxx-9xx+26x-24=0
< yields xxxx-4xxx-19xx+106x-120=0, an equation having three true
< roots 2, 3, 4, and one false root, 5."
I would have to examine it further, how he contain/isolate the arithmetic
of 'false roots'. Other way could be examining the Descartes correspondence
with other people, or mathematical literature about him
(single axis, curve contruction, the relationship of algebra and geometry, etc)
in order to have an idea of what he meant by managing false roots, different
than number line ? (it seems a rather long task...)
I wonder if exist more ways to get reciprocals.
It could take you explore more deeply the geometrical aspects to get your polysign
p4 reciprocal.
Or maybe finding some hidden additive properties/geometrical consideration
without involving product.
It sounds good Nature and springs :)
"Zero-sum permutation"
https://en.wikipedia.org/wiki/H4_polytope#Coordinates
"barycentric coordinates" "freely permuted"
Regular and Semi-Regular Polytopes II, Four-dimensional polytopes by H. Coxeter
https://en.wikipedia.org/wiki/Harold_Scott_MacDonald_Coxeter
Symmetry beyond groups by Rui Loja Fernandes
https://www.math.tecnico.ulisboa.pt/~rfern/Meus-papers/HTML/ISRLect.pdf
https://skeptics.stackexchange.com/questions/40022/did-ren%C3%A9-descartes-develop-the-cartesian-coordinate-system-by-watching-a-fly-on
The Correspondence of René Descartes 1643 edited by Theo Verbeek, Erik-Jan Bos, and Jeroen van de Ven
Rene Descartes Foundations of Analytic Geometry and Classification of Curves by Sofia Neovius
Descartes Philosophical Revolution: A Reassessment by Hanoch Ben-Yami
Historical Dictionary of Descartes and Cartesian Philosophy" by Roger Ariew, Dennis Des Chene, Douglas M. Jesseph, Tad M. Schmaltz, and Theo Verbeek
The Cambridge Descartes lexicon by Lawrence Nolan
Analysis, Synthesis, the Infinite, and Numbers by Steven Williams
A Source Book in Mathematics, 1200-1800, by Dirk Jan Struik
https://archive.org/details/B-001-001-112/page/n9/mode/2up
A History Of Mathematical Notations Vol I by Florian Cajori
https://archive.org/details/historyofmathema031756mbp
History of Analytic Geometry by Carl B. Boyer
Geometry by Its History by Alexander Ostermann and Gerhard Wanner
https://en.wikipedia.org/wiki/Grid_reference
https://en.wikipedia.org/wiki/Coordinate-free
https://en.wikipedia.org/wiki/Graph_of_a_function#Examples
https://mathworld.wolfram.com/CartesianCoordinates.html
https://hsm.stackexchange.com/questions/2372/is-it-true-that-leibniz-introduced-constant-variable-and-function
https://en.wikipedia.org/wiki/Coordinate_system#Coordinate_lines/curves_and_planes/surfaces
https://en.wikipedia.org/wiki/Curve#History
https://en.wikipedia.org/wiki/Gallery_of_curves
http://xahlee.info/surface/gallery.html
I think it may be Coxeter did study them and he may have had a name for them too. I wish they were easier to research but as I got into them through my brother's beckoning we did find a few references in time but not much. That these discrete objects are developing nearly perfect circles has to be worthy of study. As to how these details connect to ordinary affairs... it seems a long way around.
At the time of Descartes writing La Geometrie he clearly was not having negative numbers. It is just as I have alluded to before: subtraction becomes a necessary operation to perform algebra and in doing so these possibilities arise. A negative resultant is not recognized as such. It does not exist and so is called 'false'. The formalization of the real number occurred later, and our usage of 'cartesian' coordinates is a misnomer. He has bumped into the cause for real numbers and possibly did consider the exception, much as P1 seems to demand exceptional mistreatment. He also manages to bump into imaginary roots without ever needing the real value. For Descartes the signs are operators; not values. There is no positive number; there is just number. Yet his number has far more life than today's digest allows for.
answer me, why won't you use the formal construction?
Bassam Karzeddin
2020-11-02 08:20:23 UTC
Post by ***@gmail.com
Post by Tim Golden BandTech.com
Post by Lalo T.
< Book III
< ON THE CONSTRUCTION OF SOLID OR SUPERSOLID PROBLEMS
< What are false roots............ 372
< "Every equation can have as many distinct roots (values of the unknown
< quantity) as the number of dimensions of the unknown quantity in the equation.
< Suppose, for example, x=2 or x-2=0, and again, x=3, or x-3=0. Multiplying
< together the two equations x-2=0 and x-3=0, we have xx-5x+6=0, or xx=5x-6.
< This is an equation in which x has the value 2 and at the same time x has the
< value 3. If we next make x-4=0 and multiply this by xx-5x+6=0 we
< have xxx-9xx+26x-24=0 another equation, in which x, having three dimensions,
< has also three values, namely, 2, 3, and 4.
< It often happens, however, that some of the roots are false or less than
< nothing. Thus, if we suppose x to represent the defect of a quantity 5, we
< have x+5=0 which, multiplied by xxx-9xx+26x-24=0
< yields xxxx-4xxx-19xx+106x-120=0, an equation having three true
< roots 2, 3, 4, and one false root, 5."
I would have to examine it further, how he contain/isolate the arithmetic
of 'false roots'. Other way could be examining the Descartes correspondence
with other people, or mathematical literature about him
(single axis, curve contruction, the relationship of algebra and geometry, etc)
in order to have an idea of what he meant by managing false roots, different
than number line ? (it seems a rather long task...)
I wonder if exist more ways to get reciprocals.
It could take you explore more deeply the geometrical aspects to get your polysign
p4 reciprocal.
Or maybe finding some hidden additive properties/geometrical consideration
without involving product.
It sounds good Nature and springs :)
"Zero-sum permutation"
https://en.wikipedia.org/wiki/H4_polytope#Coordinates
"barycentric coordinates" "freely permuted"
Regular and Semi-Regular Polytopes II, Four-dimensional polytopes by H. Coxeter
https://en.wikipedia.org/wiki/Harold_Scott_MacDonald_Coxeter
Symmetry beyond groups by Rui Loja Fernandes
https://www.math.tecnico.ulisboa.pt/~rfern/Meus-papers/HTML/ISRLect.pdf
https://skeptics.stackexchange.com/questions/40022/did-ren%C3%A9-descartes-develop-the-cartesian-coordinate-system-by-watching-a-fly-on
The Correspondence of René Descartes 1643 edited by Theo Verbeek, Erik-Jan Bos, and Jeroen van de Ven
Rene Descartes Foundations of Analytic Geometry and Classification of Curves by Sofia Neovius
Descartes Philosophical Revolution: A Reassessment by Hanoch Ben-Yami
Historical Dictionary of Descartes and Cartesian Philosophy" by Roger Ariew, Dennis Des Chene, Douglas M. Jesseph, Tad M. Schmaltz, and Theo Verbeek
The Cambridge Descartes lexicon by Lawrence Nolan
Analysis, Synthesis, the Infinite, and Numbers by Steven Williams
A Source Book in Mathematics, 1200-1800, by Dirk Jan Struik
https://archive.org/details/B-001-001-112/page/n9/mode/2up
A History Of Mathematical Notations Vol I by Florian Cajori
https://archive.org/details/historyofmathema031756mbp
History of Analytic Geometry by Carl B. Boyer
Geometry by Its History by Alexander Ostermann and Gerhard Wanner
https://en.wikipedia.org/wiki/Grid_reference
https://en.wikipedia.org/wiki/Coordinate-free
https://en.wikipedia.org/wiki/Graph_of_a_function#Examples
https://mathworld.wolfram.com/CartesianCoordinates.html
https://hsm.stackexchange.com/questions/2372/is-it-true-that-leibniz-introduced-constant-variable-and-function
https://en.wikipedia.org/wiki/Coordinate_system#Coordinate_lines/curves_and_planes/surfaces
https://en.wikipedia.org/wiki/Curve#History
https://en.wikipedia.org/wiki/Gallery_of_curves
http://xahlee.info/surface/gallery.html
I think it may be Coxeter did study them and he may have had a name for them too. I wish they were easier to research but as I got into them through my brother's beckoning we did find a few references in time but not much. That these discrete objects are developing nearly perfect circles has to be worthy of study. As to how these details connect to ordinary affairs... it seems a long way around.
At the time of Descartes writing La Geometrie he clearly was not having negative numbers. It is just as I have alluded to before: subtraction becomes a necessary operation to perform algebra and in doing so these possibilities arise. A negative resultant is not recognized as such. It does not exist and so is called 'false'. The formalization of the real number occurred later, and our usage of 'cartesian' coordinates is a misnomer. He has bumped into the cause for real numbers and possibly did consider the exception, much as P1 seems to demand exceptional mistreatment. He also manages to bump into imaginary roots without ever needing the real value. For Descartes the signs are operators; not values. There is no positive number; there is just number. Yet his number has far more life than today's digest allows for.
answer me, why won't you use the formal construction?
*************************************************

Does it seem that recently, the anonymous professional mathematicians at *Donkeypedia** started again bounding their too lengthy business about what is a real number?

With tons of many alleged historical references (as always as usual)

Now they are recognizing that even the word positive doesn't have true meaning since it came after inventing the untrue negative numbers

Look carefully how many older threads I wrote about it with full details and simple numerical examples

They are realizing now that negative and imaginary numbers are human mind fart numbers (as I exactly did in so many published threads before them)

As a reminder, soon they would certainly **REDISCOVER** the same things that I did discover about the non-existence of the non-constructible numbers

But their ways are toooooo.... lengthy business with tons of fabricated and forged historical references since if it was true, why didn't it being discussed years before it comes suddenly nowadays

How come in the very shameful history of mathematics that someone who isn't a specialist but only a mature announces many unusual facts (with many irrefutable elementary proofs) in public sources where everybody stubbornly denies and suddenly later an army of annymous expert professional academic mathematicians and alike start a too lengthy business announcing his own points of views and **SUDDENLYY** finding many older historical references as well to cover up the entire holes that an amateur had only pointed out in public sources much before their too long tongs started their business

As a reminder for their coming discoveries (not frankly announced yet)

1) They would soon **REDISCOVER** suddenly that the Cardano formula is quite **FALSE** as exactly as I did

2) They would soon **REDISCOVER** suddenly that (Galois, Ruffanee and Aple)
the theorem is also **FALSE** as exactly as I did

3) They would soon **REDISCOVER** suddenly that the endless act of (Dedikuned cuts, Cauchy sequences, Intermediate theorems, Limits, Convergence, ..., etc) can't define truly a single real existing (constructible) number), as exactly as I did

4) They would soon **REDISCOVER** suddenly that the vast majorities of the well-known angles in both old and modern mathematics don't even exist, as exactly as I did

5) They would soon **REDISCOVER** suddenly that the true existing numbers are only those described in the standard mathematics as positive constructible numbers, as exactly as I did

6) They would soon **REDISCOVER** suddenly that the most worshipped human mind numbers (pi, e, 0 and the cube root of a prime number) aren't real nor existing numbers, as exactly as I did

7)They would soon **REDISCOVER** suddenly that the imaginary numbers were a very false decision as exactly as I did

8) They would soon **REDISCOVER** suddenly that continuity of real numbers don't exist and the real (constructible) numbers are discrete numbers, as exactly as I did

9) They would soon **REDISCOVER** suddenly that the Euclidean space is the only true spaces were curved space or spacetime is a fart idea, as exactly as I did

10) They would soon **REDISCOVER** suddenly that the Non-Euclidean geometry exists only in Euclidean geometry as exactly as I did

11) They would soon **REDISCOVER** suddenly that the true solution to the three impossible constructin problems raised by the ancient Greeks are impossible constructions by any tools or means since nither the circle nor the cube root two is an existing mathematical object as exactly as I did

12) They would soon **REDISCOVER** suddenly that the compass is never a valid tool to make a circle, as exactly as I did

13) They would soon **REDISCOVER** suddenly that (0.999...) isn't a number and as exactly as I did in older posts beside few other members of sci. math as JG

....
....

This is the true hidden purpose of that "Wikipedia" with most of their hired members 'anonymous' writers who seemingly contributing freely and generously to the whole world freely

The main idea behind all that activity is "NOTHING' must be ever taken from any public sources (as long as there are masters in top-most alleged reputable Journals and Universities), no matter if that public source is a true remedy to most of their top riddles

Let us hope that this would remain as a wonderful piece of shred evidence for truer natural historical purposes in the near future

This is the ugly fact about the alleged nobility of the academic people of this particular century (under the sunlight) and in an era of global immediate communication that is as fast as light (with no wounders)

Bassam Karzeddin
zelos...@gmail.com
2020-11-02 08:32:14 UTC
Post by Bassam Karzeddin
Does it seem that recently, the anonymous professional mathematicians at *Donkeypedia** started again bounding their too lengthy business about what is a real number?
You hate wikipedia cause it shows you wrong.
Post by Bassam Karzeddin
Now they are recognizing that even the word positive doesn't have true meaning since it came after inventing the untrue negative numbers
Negative numbers can be constructed, get over it.
Post by Bassam Karzeddin
Look carefully how many older threads I wrote about it with full details and simple numerical examples
You have never demonstrated their non-existence because you cannot show a contradiction.
Post by Bassam Karzeddin
They are realizing now that negative and imaginary numbers are human mind fart numbers (as I exactly did in so many published threads before them)
All numbers are made in our minds.
Post by Bassam Karzeddin
1) They would soon **REDISCOVER** suddenly that the Cardano formula is quite **FALSE** as exactly as I did
Except it is demonstrably correct so tough shit.
Post by Bassam Karzeddin
2) They would soon **REDISCOVER** suddenly that (Galois, Ruffanee and Aple) the theorem is also **FALSE** as exactly as I did
except they are demonstrably true.
Post by Bassam Karzeddin
3) They would soon **REDISCOVER** suddenly that the endless act of (Dedikuned cuts, Cauchy sequences, Intermediate theorems, Limits, Convergence, ..., etc) can't define truly a single real existing (constructible) number), as exactly as I did
Except we can show that they do give real number structures so tough shit. You're wrong.
Post by Bassam Karzeddin
4) They would soon **REDISCOVER** suddenly that the vast majorities of the well-known angles in both old and modern mathematics don't even exist, as exactly as I did
Its all just real numbers so you are simply wrong here.
Post by Bassam Karzeddin
5) They would soon **REDISCOVER** suddenly that the true existing numbers are only those described in the standard mathematics as positive constructible numbers, as exactly as I did
Why would those be the only numbers? That is your idiotic idea, not mathematics.
Post by Bassam Karzeddin
6) They would soon **REDISCOVER** suddenly that the most worshipped human mind numbers (pi, e, 0 and the cube root of a prime number) aren't real nor existing numbers, as exactly as I did
Except we can construct all of them so tough shit.
Post by Bassam Karzeddin
7)They would soon **REDISCOVER** suddenly that the imaginary numbers were a very false decision as exactly as I did
Except its used and useful and we can easily construct it using |R[x]/<x^2+1> so exist it does.

8) They would soon **REDISCOVER** suddenly that continuity of real numbers don't exist and the real (constructible) numbers are discrete numbers, as exactly as I did

Even in rational numbers, it ain't discrete you moron.
Post by Bassam Karzeddin
9) They would soon **REDISCOVER** suddenly that the Euclidean space is the only true spaces were curved space or spacetime is a fart idea, as exactly as I did
Except we know space is curved both on earth adn the actual spacetime and euclidean cannot account or describe them so.
Post by Bassam Karzeddin
10) They would soon **REDISCOVER** suddenly that the Non-Euclidean geometry exists only in Euclidean geometry as exactly as I did
It is not in it cause they require statements that are false in euclidean you imbecile.
Post by Bassam Karzeddin
11) They would soon **REDISCOVER** suddenly that the true solution to the three impossible constructin problems raised by the ancient Greeks are impossible constructions by any tools or means since nither the circle nor the cube root two is an existing mathematical object as exactly as I did
That's not why they are impossible you imbecile.
Post by Bassam Karzeddin
12) They would soon **REDISCOVER** suddenly that the compass is never a valid tool to make a circle, as exactly as I did
This is your claim, but not valid.
Post by Bassam Karzeddin
13) They would soon **REDISCOVER** suddenly that (0.999...) isn't a number and as exactly as I did in older posts beside few other members of sci. math as JG
Citing a infamous crank like Gabriel weakens your position, not strengthen.
Bassam Karzeddin
2020-11-02 09:20:30 UTC
Post by ***@gmail.com
Post by Bassam Karzeddin
Does it seem that recently, the anonymous professional mathematicians at *Donkeypedia** started again bounding their too lengthy business about what is a real number?
You hate wikipedia cause it shows you wrong.
Post by Bassam Karzeddin
Now they are recognizing that even the word positive doesn't have true meaning since it came after inventing the untrue negative numbers
Negative numbers can be constructed, get over it.
Post by Bassam Karzeddin
Look carefully how many older threads I wrote about it with full details and simple numerical examples
You have never demonstrated their non-existence because you cannot show a contradiction.
Post by Bassam Karzeddin
They are realizing now that negative and imaginary numbers are human mind fart numbers (as I exactly did in so many published threads before them)
All numbers are made in our minds.
Post by Bassam Karzeddin
1) They would soon **REDISCOVER** suddenly that the Cardano formula is quite **FALSE** as exactly as I did
Except it is demonstrably correct so tough shit.
Post by Bassam Karzeddin
2) They would soon **REDISCOVER** suddenly that (Galois, Ruffanee and Aple) the theorem is also **FALSE** as exactly as I did
except they are demonstrably true.
Post by Bassam Karzeddin
3) They would soon **REDISCOVER** suddenly that the endless act of (Dedikuned cuts, Cauchy sequences, Intermediate theorems, Limits, Convergence, ..., etc) can't define truly a single real existing (constructible) number), as exactly as I did
Except we can show that they do give real number structures so tough shit. You're wrong.
Post by Bassam Karzeddin
4) They would soon **REDISCOVER** suddenly that the vast majorities of the well-known angles in both old and modern mathematics don't even exist, as exactly as I did
Its all just real numbers so you are simply wrong here.
Post by Bassam Karzeddin
5) They would soon **REDISCOVER** suddenly that the true existing numbers are only those described in the standard mathematics as positive constructible numbers, as exactly as I did
Why would those be the only numbers? That is your idiotic idea, not mathematics.
Post by Bassam Karzeddin
6) They would soon **REDISCOVER** suddenly that the most worshipped human mind numbers (pi, e, 0 and the cube root of a prime number) aren't real nor existing numbers, as exactly as I did
Except we can construct all of them so tough shit.
Post by Bassam Karzeddin
7)They would soon **REDISCOVER** suddenly that the imaginary numbers were a very false decision as exactly as I did
Except its used and useful and we can easily construct it using |R[x]/<x^2+1> so exist it does.
8) They would soon **REDISCOVER** suddenly that continuity of real numbers don't exist and the real (constructible) numbers are discrete numbers, as exactly as I did
Even in rational numbers, it ain't discrete you moron.
Post by Bassam Karzeddin
9) They would soon **REDISCOVER** suddenly that the Euclidean space is the only true spaces were curved space or spacetime is a fart idea, as exactly as I did
Except we know space is curved both on earth adn the actual spacetime and euclidean cannot account or describe them so.
Post by Bassam Karzeddin
10) They would soon **REDISCOVER** suddenly that the Non-Euclidean geometry exists only in Euclidean geometry as exactly as I did
It is not in it cause they require statements that are false in euclidean you imbecile.
Post by Bassam Karzeddin
11) They would soon **REDISCOVER** suddenly that the true solution to the three impossible constructin problems raised by the ancient Greeks are impossible constructions by any tools or means since nither the circle nor the cube root two is an existing mathematical object as exactly as I did
That's not why they are impossible you imbecile.
Post by Bassam Karzeddin
12) They would soon **REDISCOVER** suddenly that the compass is never a valid tool to make a circle, as exactly as I did
This is your claim, but not valid.
Post by Bassam Karzeddin
13) They would soon **REDISCOVER** suddenly that (0.999...) isn't a number and as exactly as I did in older posts beside few other members of sci. math as JG
Citing a infamous crank like Gabriel weakens your position, not strengthen.
A dipshit incurable academic troll and imbecile mathematiker Zelos is

Well-certified by many members as a Physico severe mental case who always bring the worst of maths he had blindly inherited

Can't get a hint yet to what is truly happening nowadays in mathematics on the top-levels with many references before his own eyes

He is certainly a hired troll who fails usually to convince anyone about anything of his old inherited false beliefs

If (7 - 3 - 4 = 0) is a deformed shape of an original natural numerical equation like this (7 = 3 + 4), and without zero and without negatives

So, where are your zero and negative Moron

It is the seventh impossible to correctly communicate only with such common academic mathematicians like Zelos about such a very fundamental issue

Who cares for your nonsense Moron?

You can't get any hint yet and you shouldn't for sure

My issues are not meant for your likes Zelos Malume Idiot

BKK
zelos...@gmail.com
2020-11-02 09:51:08 UTC
Post by Bassam Karzeddin
A dipshit incurable academic troll and imbecile mathematiker Zelos is
Pointing out when/where you are wrong does not make me a troll :)
Post by Bassam Karzeddin
He is certainly a hired troll who fails usually to convince anyone about anything of his old inherited false beliefs
I am not hired, I get pleasure from showing you wrong :)
Post by Bassam Karzeddin
If (7 - 3 - 4 = 0) is a deformed shape of an original natural numerical equation like this (7 = 3 + 4), and without zero and without negatives
Both are equivalent, so what?
Post by Bassam Karzeddin
So, where are your zero and negative Moron
Just because you can rewrite thigns does that not make them disapepar.
Post by Bassam Karzeddin
Who cares for your nonsense Moron?
Nonsense comes from you, I give proper mathematics, ever tried learnign it?
Timothy Golden
2020-11-04 14:07:58 UTC
Post by Bassam Karzeddin
Post by ***@gmail.com
Post by Bassam Karzeddin
Does it seem that recently, the anonymous professional mathematicians at *Donkeypedia** started again bounding their too lengthy business about what is a real number?
You hate wikipedia cause it shows you wrong.
Post by Bassam Karzeddin
Now they are recognizing that even the word positive doesn't have true meaning since it came after inventing the untrue negative numbers
Negative numbers can be constructed, get over it.
Post by Bassam Karzeddin
Look carefully how many older threads I wrote about it with full details and simple numerical examples
You have never demonstrated their non-existence because you cannot show a contradiction.
Post by Bassam Karzeddin
They are realizing now that negative and imaginary numbers are human mind fart numbers (as I exactly did in so many published threads before them)
All numbers are made in our minds.
Post by Bassam Karzeddin
1) They would soon **REDISCOVER** suddenly that the Cardano formula is quite **FALSE** as exactly as I did
Except it is demonstrably correct so tough shit.
Post by Bassam Karzeddin
2) They would soon **REDISCOVER** suddenly that (Galois, Ruffanee and Aple) the theorem is also **FALSE** as exactly as I did
except they are demonstrably true.
Post by Bassam Karzeddin
3) They would soon **REDISCOVER** suddenly that the endless act of (Dedikuned cuts, Cauchy sequences, Intermediate theorems, Limits, Convergence, ..., etc) can't define truly a single real existing (constructible) number), as exactly as I did
Except we can show that they do give real number structures so tough shit. You're wrong.
Post by Bassam Karzeddin
4) They would soon **REDISCOVER** suddenly that the vast majorities of the well-known angles in both old and modern mathematics don't even exist, as exactly as I did
Its all just real numbers so you are simply wrong here.
Post by Bassam Karzeddin
5) They would soon **REDISCOVER** suddenly that the true existing numbers are only those described in the standard mathematics as positive constructible numbers, as exactly as I did
Why would those be the only numbers? That is your idiotic idea, not mathematics.
Post by Bassam Karzeddin
6) They would soon **REDISCOVER** suddenly that the most worshipped human mind numbers (pi, e, 0 and the cube root of a prime number) aren't real nor existing numbers, as exactly as I did
Except we can construct all of them so tough shit.
Post by Bassam Karzeddin
7)They would soon **REDISCOVER** suddenly that the imaginary numbers were a very false decision as exactly as I did
Except its used and useful and we can easily construct it using |R[x]/<x^2+1> so exist it does.
8) They would soon **REDISCOVER** suddenly that continuity of real numbers don't exist and the real (constructible) numbers are discrete numbers, as exactly as I did
Even in rational numbers, it ain't discrete you moron.
Post by Bassam Karzeddin
9) They would soon **REDISCOVER** suddenly that the Euclidean space is the only true spaces were curved space or spacetime is a fart idea, as exactly as I did
Except we know space is curved both on earth adn the actual spacetime and euclidean cannot account or describe them so.
Post by Bassam Karzeddin
10) They would soon **REDISCOVER** suddenly that the Non-Euclidean geometry exists only in Euclidean geometry as exactly as I did
It is not in it cause they require statements that are false in euclidean you imbecile.
Post by Bassam Karzeddin
11) They would soon **REDISCOVER** suddenly that the true solution to the three impossible constructin problems raised by the ancient Greeks are impossible constructions by any tools or means since nither the circle nor the cube root two is an existing mathematical object as exactly as I did
That's not why they are impossible you imbecile.
Post by Bassam Karzeddin
12) They would soon **REDISCOVER** suddenly that the compass is never a valid tool to make a circle, as exactly as I did
This is your claim, but not valid.
Post by Bassam Karzeddin
13) They would soon **REDISCOVER** suddenly that (0.999...) isn't a number and as exactly as I did in older posts beside few other members of sci. math as JG
Citing a infamous crank like Gabriel weakens your position, not strengthen.
A dipshit incurable academic troll and imbecile mathematiker Zelos is
Well-certified by many members as a Physico severe mental case who always bring the worst of maths he had blindly inherited
Can't get a hint yet to what is truly happening nowadays in mathematics on the top-levels with many references before his own eyes
He is certainly a hired troll who fails usually to convince anyone about anything of his old inherited false beliefs
If (7 - 3 - 4 = 0) is a deformed shape of an original natural numerical equation like this (7 = 3 + 4), and without zero and without negatives
So, where are your zero and negative Moron
It is the seventh impossible to correctly communicate only with such common academic mathematicians like Zelos about such a very fundamental issue
Who cares for your nonsense Moron?
You can't get any hint yet and you shouldn't for sure
My issues are not meant for your likes Zelos Malume Idiot
BKK
I do feel as though I am about as extreme as the 'standard' USENET (ab)user here on sci.math. But really I try to treat these topics as open. I ask that you who are unafraid to criticize likewise be unafraid to construct. This is a freedom that we all must grant ourselves, yet it is nothing like the burden of accountability as we sat in classrooms knowing that if we failed to mimic the presentation that we would be offed. As I read the lines of rejectional thinking here I can't help but expose the trap of academia.

Our way here can be errant. In fact it is by being errant that we yield corrective measures. Now within the curriculum this has occured too. Abstract Algebra denies the necessity of subtraction as an operator, yet it is the first instance of how we can bump into the negative number. Subtraction also happens to be asymmetrical:
4 - 3 =/= 3 - 4
and indeed the only time that symmetry can be had is when
+ 2 - 2 = 0 = - 2 + 2
and strangely enough this is extremely near to polysign's own requirements. Now of course in these arithmetic systems there lays many an interpretation that ultimately are equivalent and hence a list of six or so formal constructions of the real number. I didn't really mean to go here so let's just put a 'todo' on this one. Possibly there is a more convincing route to polysign here though for me it seems indirect. That is irrelevant though; if it guides people into polysign then some criterion of value is had.

More to the point is that abstract algebra in some ways is a return to Descarte's false roots. But the signs are now in the values so subtraction is merely the addition of the inverse and all is well... except that we are free to develop interpretations on these goings on. The value of these interpretations can be meaningful if variations arise from their analysis. Just one minor fleck formalized could turn the math world to its knees. I know we all want to take it there. It is a hideous beast of snotty professors bordering on theologists. They are the perfect mimics. They are the problem. Obviously they didn't set out to be that way. Then too there are the journals... a level up in the hierarchy. Openness is not their strong suit. Criticism of the topic at hand or personal philosophy will not be put on the lectern, or if they are it will be done with great care so as not to upset their neighbors. We are the fortunate ones who arrive here in an uncensored space; who remain powerless; who are allowed to make mistakes!

Addition is integration is superpostion is fundamental. Multiplication is not so. It may mimic it and we may do it, but the fundamental sensibility of it is lost particularly within geometrical representations. The notion that
a b
exists in the same set as a and as b is not actually what we observe. Well then is this physics or is this mathematics? Of course I see that question as asinine. Is this philosophy or mathematics?

The sum is just
The product not so
And of the X many say much
zelos...@gmail.com
2020-11-04 14:18:14 UTC
Post by Timothy Golden
Post by Bassam Karzeddin
Post by ***@gmail.com
Post by Bassam Karzeddin
Does it seem that recently, the anonymous professional mathematicians at *Donkeypedia** started again bounding their too lengthy business about what is a real number?
You hate wikipedia cause it shows you wrong.
Post by Bassam Karzeddin
Now they are recognizing that even the word positive doesn't have true meaning since it came after inventing the untrue negative numbers
Negative numbers can be constructed, get over it.
Post by Bassam Karzeddin
Look carefully how many older threads I wrote about it with full details and simple numerical examples
You have never demonstrated their non-existence because you cannot show a contradiction.
Post by Bassam Karzeddin
They are realizing now that negative and imaginary numbers are human mind fart numbers (as I exactly did in so many published threads before them)
All numbers are made in our minds.
Post by Bassam Karzeddin
1) They would soon **REDISCOVER** suddenly that the Cardano formula is quite **FALSE** as exactly as I did
Except it is demonstrably correct so tough shit.
Post by Bassam Karzeddin
2) They would soon **REDISCOVER** suddenly that (Galois, Ruffanee and Aple) the theorem is also **FALSE** as exactly as I did
except they are demonstrably true.
Post by Bassam Karzeddin
3) They would soon **REDISCOVER** suddenly that the endless act of (Dedikuned cuts, Cauchy sequences, Intermediate theorems, Limits, Convergence, ..., etc) can't define truly a single real existing (constructible) number), as exactly as I did
Except we can show that they do give real number structures so tough shit. You're wrong.
Post by Bassam Karzeddin
4) They would soon **REDISCOVER** suddenly that the vast majorities of the well-known angles in both old and modern mathematics don't even exist, as exactly as I did
Its all just real numbers so you are simply wrong here.
Post by Bassam Karzeddin
5) They would soon **REDISCOVER** suddenly that the true existing numbers are only those described in the standard mathematics as positive constructible numbers, as exactly as I did
Why would those be the only numbers? That is your idiotic idea, not mathematics.
Post by Bassam Karzeddin
6) They would soon **REDISCOVER** suddenly that the most worshipped human mind numbers (pi, e, 0 and the cube root of a prime number) aren't real nor existing numbers, as exactly as I did
Except we can construct all of them so tough shit.
Post by Bassam Karzeddin
7)They would soon **REDISCOVER** suddenly that the imaginary numbers were a very false decision as exactly as I did
Except its used and useful and we can easily construct it using |R[x]/<x^2+1> so exist it does.
8) They would soon **REDISCOVER** suddenly that continuity of real numbers don't exist and the real (constructible) numbers are discrete numbers, as exactly as I did
Even in rational numbers, it ain't discrete you moron.
Post by Bassam Karzeddin
9) They would soon **REDISCOVER** suddenly that the Euclidean space is the only true spaces were curved space or spacetime is a fart idea, as exactly as I did
Except we know space is curved both on earth adn the actual spacetime and euclidean cannot account or describe them so.
Post by Bassam Karzeddin
10) They would soon **REDISCOVER** suddenly that the Non-Euclidean geometry exists only in Euclidean geometry as exactly as I did
It is not in it cause they require statements that are false in euclidean you imbecile.
Post by Bassam Karzeddin
11) They would soon **REDISCOVER** suddenly that the true solution to the three impossible constructin problems raised by the ancient Greeks are impossible constructions by any tools or means since nither the circle nor the cube root two is an existing mathematical object as exactly as I did
That's not why they are impossible you imbecile.
Post by Bassam Karzeddin
12) They would soon **REDISCOVER** suddenly that the compass is never a valid tool to make a circle, as exactly as I did
This is your claim, but not valid.
Post by Bassam Karzeddin
13) They would soon **REDISCOVER** suddenly that (0.999...) isn't a number and as exactly as I did in older posts beside few other members of sci. math as JG
Citing a infamous crank like Gabriel weakens your position, not strengthen.
A dipshit incurable academic troll and imbecile mathematiker Zelos is
Well-certified by many members as a Physico severe mental case who always bring the worst of maths he had blindly inherited
Can't get a hint yet to what is truly happening nowadays in mathematics on the top-levels with many references before his own eyes
He is certainly a hired troll who fails usually to convince anyone about anything of his old inherited false beliefs
If (7 - 3 - 4 = 0) is a deformed shape of an original natural numerical equation like this (7 = 3 + 4), and without zero and without negatives
So, where are your zero and negative Moron
It is the seventh impossible to correctly communicate only with such common academic mathematicians like Zelos about such a very fundamental issue
Who cares for your nonsense Moron?
You can't get any hint yet and you shouldn't for sure
My issues are not meant for your likes Zelos Malume Idiot
BKK
I do feel as though I am about as extreme as the 'standard' USENET (ab)user here on sci.math. But really I try to treat these topics as open. I ask that you who are unafraid to criticize likewise be unafraid to construct. This is a freedom that we all must grant ourselves, yet it is nothing like the burden of accountability as we sat in classrooms knowing that if we failed to mimic the presentation that we would be offed. As I read the lines of rejectional thinking here I can't help but expose the trap of academia.
4 - 3 =/= 3 - 4
and indeed the only time that symmetry can be had is when
+ 2 - 2 = 0 = - 2 + 2
and strangely enough this is extremely near to polysign's own requirements. Now of course in these arithmetic systems there lays many an interpretation that ultimately are equivalent and hence a list of six or so formal constructions of the real number. I didn't really mean to go here so let's just put a 'todo' on this one. Possibly there is a more convincing route to polysign here though for me it seems indirect. That is irrelevant though; if it guides people into polysign then some criterion of value is had.
More to the point is that abstract algebra in some ways is a return to Descarte's false roots. But the signs are now in the values so subtraction is merely the addition of the inverse and all is well... except that we are free to develop interpretations on these goings on. The value of these interpretations can be meaningful if variations arise from their analysis. Just one minor fleck formalized could turn the math world to its knees. I know we all want to take it there. It is a hideous beast of snotty professors bordering on theologists. They are the perfect mimics. They are the problem. Obviously they didn't set out to be that way. Then too there are the journals... a level up in the hierarchy. Openness is not their strong suit. Criticism of the topic at hand or personal philosophy will not be put on the lectern, or if they are it will be done with great care so as not to upset their neighbors. We are the fortunate ones who arrive here in an uncensored space; who remain powerless; who are allowed to make mistakes!
Addition is integration is superpostion is fundamental. Multiplication is not so. It may mimic it and we may do it, but the fundamental sensibility of it is lost particularly within geometrical representations. The notion that
a b
exists in the same set as a and as b is not actually what we observe. Well then is this physics or is this mathematics? Of course I see that question as asinine. Is this philosophy or mathematics?
The sum is just
The product not so
And of the X many say much
things are open in mathematics, the issue is you gotta come with legitimate things. You don't by complaining no notation.
Bassam Karzeddin
2020-11-05 07:45:43 UTC
Post by Timothy Golden
Post by Bassam Karzeddin
Post by ***@gmail.com
Post by Bassam Karzeddin
Does it seem that recently, the anonymous professional mathematicians at *Donkeypedia** started again bounding their too lengthy business about what is a real number?
You hate wikipedia cause it shows you wrong.
Post by Bassam Karzeddin
Now they are recognizing that even the word positive doesn't have true meaning since it came after inventing the untrue negative numbers
Negative numbers can be constructed, get over it.
Post by Bassam Karzeddin
Look carefully how many older threads I wrote about it with full details and simple numerical examples
You have never demonstrated their non-existence because you cannot show a contradiction.
Post by Bassam Karzeddin
They are realizing now that negative and imaginary numbers are human mind fart numbers (as I exactly did in so many published threads before them)
All numbers are made in our minds.
Post by Bassam Karzeddin
1) They would soon **REDISCOVER** suddenly that the Cardano formula is quite **FALSE** as exactly as I did
Except it is demonstrably correct so tough shit.
Post by Bassam Karzeddin
2) They would soon **REDISCOVER** suddenly that (Galois, Ruffanee and Aple) the theorem is also **FALSE** as exactly as I did
except they are demonstrably true.
Post by Bassam Karzeddin
3) They would soon **REDISCOVER** suddenly that the endless act of (Dedikuned cuts, Cauchy sequences, Intermediate theorems, Limits, Convergence, ..., etc) can't define truly a single real existing (constructible) number), as exactly as I did
Except we can show that they do give real number structures so tough shit. You're wrong.
Post by Bassam Karzeddin
4) They would soon **REDISCOVER** suddenly that the vast majorities of the well-known angles in both old and modern mathematics don't even exist, as exactly as I did
Its all just real numbers so you are simply wrong here.
Post by Bassam Karzeddin
5) They would soon **REDISCOVER** suddenly that the true existing numbers are only those described in the standard mathematics as positive constructible numbers, as exactly as I did
Why would those be the only numbers? That is your idiotic idea, not mathematics.
Post by Bassam Karzeddin
6) They would soon **REDISCOVER** suddenly that the most worshipped human mind numbers (pi, e, 0 and the cube root of a prime number) aren't real nor existing numbers, as exactly as I did
Except we can construct all of them so tough shit.
Post by Bassam Karzeddin
7)They would soon **REDISCOVER** suddenly that the imaginary numbers were a very false decision as exactly as I did
Except its used and useful and we can easily construct it using |R[x]/<x^2+1> so exist it does.
8) They would soon **REDISCOVER** suddenly that continuity of real numbers don't exist and the real (constructible) numbers are discrete numbers, as exactly as I did
Even in rational numbers, it ain't discrete you moron.
Post by Bassam Karzeddin
9) They would soon **REDISCOVER** suddenly that the Euclidean space is the only true spaces were curved space or spacetime is a fart idea, as exactly as I did
Except we know space is curved both on earth adn the actual spacetime and euclidean cannot account or describe them so.
Post by Bassam Karzeddin
10) They would soon **REDISCOVER** suddenly that the Non-Euclidean geometry exists only in Euclidean geometry as exactly as I did
It is not in it cause they require statements that are false in euclidean you imbecile.
Post by Bassam Karzeddin
11) They would soon **REDISCOVER** suddenly that the true solution to the three impossible constructin problems raised by the ancient Greeks are impossible constructions by any tools or means since nither the circle nor the cube root two is an existing mathematical object as exactly as I did
That's not why they are impossible you imbecile.
Post by Bassam Karzeddin
12) They would soon **REDISCOVER** suddenly that the compass is never a valid tool to make a circle, as exactly as I did
This is your claim, but not valid.
Post by Bassam Karzeddin
13) They would soon **REDISCOVER** suddenly that (0.999...) isn't a number and as exactly as I did in older posts beside few other members of sci. math as JG
Citing a infamous crank like Gabriel weakens your position, not strengthen.
A dipshit incurable academic troll and imbecile mathematiker Zelos is
Well-certified by many members as a Physico severe mental case who always bring the worst of maths he had blindly inherited
Can't get a hint yet to what is truly happening nowadays in mathematics on the top-levels with many references before his own eyes
He is certainly a hired troll who fails usually to convince anyone about anything of his old inherited false beliefs
If (7 - 3 - 4 = 0) is a deformed shape of an original natural numerical equation like this (7 = 3 + 4), and without zero and without negatives
So, where are your zero and negative Moron
It is the seventh impossible to correctly communicate only with such common academic mathematicians like Zelos about such a very fundamental issue
Who cares for your nonsense Moron?
You can't get any hint yet and you shouldn't for sure
My issues are not meant for your likes Zelos Malume Idiot
BKK
I do feel as though I am about as extreme as the 'standard' USENET (ab)user here on sci.math. But really I try to treat these topics as open. I ask that you who are unafraid to criticize likewise be unafraid to construct. This is a freedom that we all must grant ourselves, yet it is nothing like the burden of accountability as we sat in classrooms knowing that if we failed to mimic the presentation that we would be offed. As I read the lines of rejectional thinking here I can't help but expose the trap of academia.
4 - 3 =/= 3 - 4
and indeed the only time that symmetry can be had is when
+ 2 - 2 = 0 = - 2 + 2
Please Note something doubtful here about creating unnecessary illegal number like zero

Naturally, with significant integers or natural numbers (n), described as positive integers in standard mathematics, we have (n = n), which is a very meaningless equation, so like we have (2 = 2), without an unnecessary human brain fart

Then why the hell we should rewrite the same nonsense (2=2) into other larger nonsense like this (2 - 2 = 0), adding unnecessay the negative operation and a non-existing number like zero? wounders!

And furher go to the negatives and create many illegal babies numbers like the imaginaries and more the complex numbers and further many more incomprehensible riddles arise the Raymond hypothesis and many more just because the older generations of mathematicians wanted to generate theorems that should benefit them only on the shoulders of all humans so illegally I must admit

In fact, most of the current mathematical riddles that are bothering the mathematicians for many centuries are purely fake and resulting from their own illegal thinking and they are entirely pure human mind cheat mainly for entertaining

Not to mention how bad that was reflected in many other theoretical sciences like the physics which uses such wrong concept in mathematics to come up suddenly with negative mass, the maximum speed of light, and soon the imaginary mass or energy and alike with many universes as well to a limit of adding so many legendary stories that any religion would be very ashamed of to include

Of course, there are truer and older mathematical puzzles that are strictly in number theory still standing for centuries and thousands of years as well

So, the best-alleged living mathematicians generally aren't aware of how harmful and too dangerous their own shallow and hollow thinking on the entire humanity as an inevitable result (where luckily for them, this is very away from any wide public attention in this century)

Regards

Bassam Karzeddin
Post by Timothy Golden
and strangely enough this is extremely near to polysign's own requirements. Now of course in these arithmetic systems there lays many an interpretation that ultimately are equivalent and hence a list of six or so formal constructions of the real number. I didn't really mean to go here so let's just put a 'todo' on this one. Possibly there is a more convincing route to polysign here though for me it seems indirect. That is irrelevant though; if it guides people into polysign then some criterion of value is had.
More to the point is that abstract algebra in some ways is a return to Descarte's false roots. But the signs are now in the values so subtraction is merely the addition of the inverse and all is well... except that we are free to develop interpretations on these goings on. The value of these interpretations can be meaningful if variations arise from their analysis. Just one minor fleck formalized could turn the math world to its knees. I know we all want to take it there. It is a hideous beast of snotty professors bordering on theologists. They are the perfect mimics. They are the problem. Obviously they didn't set out to be that way. Then too there are the journals... a level up in the hierarchy. Openness is not their strong suit. Criticism of the topic at hand or personal philosophy will not be put on the lectern, or if they are it will be done with great care so as not to upset their neighbors. We are the fortunate ones who arrive here in an uncensored space; who remain powerless; who are allowed to make mistakes!
Addition is integration is superpostion is fundamental. Multiplication is not so. It may mimic it and we may do it, but the fundamental sensibility of it is lost particularly within geometrical representations. The notion that
a b
exists in the same set as a and as b is not actually what we observe. Well then is this physics or is this mathematics? Of course I see that question as asinine. Is this philosophy or mathematics?
The sum is just
The product not so
And of the X many say much
zelos...@gmail.com
2020-11-05 08:23:26 UTC
Post by Bassam Karzeddin
Please Note something doubtful here about creating unnecessary illegal number like zero
There is no law in the world that zero would violate and it is certainly not unecessary cause it is very very useful.
Post by Bassam Karzeddin
In fact, most of the current mathematical riddles that are bothering the mathematicians for many centuries are purely fake and resulting from their own illegal thinking and they are entirely pure human mind cheat mainly for entertaining
You just hate that you are far too dumb to understand it
Timothy Golden
2020-11-05 16:53:16 UTC
Post by Bassam Karzeddin
Post by Timothy Golden
Post by Bassam Karzeddin
Post by ***@gmail.com
Post by Bassam Karzeddin
Does it seem that recently, the anonymous professional mathematicians at *Donkeypedia** started again bounding their too lengthy business about what is a real number?
You hate wikipedia cause it shows you wrong.
Post by Bassam Karzeddin
Now they are recognizing that even the word positive doesn't have true meaning since it came after inventing the untrue negative numbers
Negative numbers can be constructed, get over it.
Post by Bassam Karzeddin
Look carefully how many older threads I wrote about it with full details and simple numerical examples
You have never demonstrated their non-existence because you cannot show a contradiction.
Post by Bassam Karzeddin
They are realizing now that negative and imaginary numbers are human mind fart numbers (as I exactly did in so many published threads before them)
All numbers are made in our minds.
Post by Bassam Karzeddin
1) They would soon **REDISCOVER** suddenly that the Cardano formula is quite **FALSE** as exactly as I did
Except it is demonstrably correct so tough shit.
Post by Bassam Karzeddin
2) They would soon **REDISCOVER** suddenly that (Galois, Ruffanee and Aple) the theorem is also **FALSE** as exactly as I did
except they are demonstrably true.
Post by Bassam Karzeddin
3) They would soon **REDISCOVER** suddenly that the endless act of (Dedikuned cuts, Cauchy sequences, Intermediate theorems, Limits, Convergence, ..., etc) can't define truly a single real existing (constructible) number), as exactly as I did
Except we can show that they do give real number structures so tough shit. You're wrong.
Post by Bassam Karzeddin
4) They would soon **REDISCOVER** suddenly that the vast majorities of the well-known angles in both old and modern mathematics don't even exist, as exactly as I did
Its all just real numbers so you are simply wrong here.
Post by Bassam Karzeddin
5) They would soon **REDISCOVER** suddenly that the true existing numbers are only those described in the standard mathematics as positive constructible numbers, as exactly as I did
Why would those be the only numbers? That is your idiotic idea, not mathematics.
Post by Bassam Karzeddin
6) They would soon **REDISCOVER** suddenly that the most worshipped human mind numbers (pi, e, 0 and the cube root of a prime number) aren't real nor existing numbers, as exactly as I did
Except we can construct all of them so tough shit.
Post by Bassam Karzeddin
7)They would soon **REDISCOVER** suddenly that the imaginary numbers were a very false decision as exactly as I did
Except its used and useful and we can easily construct it using |R[x]/<x^2+1> so exist it does.
8) They would soon **REDISCOVER** suddenly that continuity of real numbers don't exist and the real (constructible) numbers are discrete numbers, as exactly as I did
Even in rational numbers, it ain't discrete you moron.
Post by Bassam Karzeddin
9) They would soon **REDISCOVER** suddenly that the Euclidean space is the only true spaces were curved space or spacetime is a fart idea, as exactly as I did
Except we know space is curved both on earth adn the actual spacetime and euclidean cannot account or describe them so.
Post by Bassam Karzeddin
10) They would soon **REDISCOVER** suddenly that the Non-Euclidean geometry exists only in Euclidean geometry as exactly as I did
It is not in it cause they require statements that are false in euclidean you imbecile.
Post by Bassam Karzeddin
11) They would soon **REDISCOVER** suddenly that the true solution to the three impossible constructin problems raised by the ancient Greeks are impossible constructions by any tools or means since nither the circle nor the cube root two is an existing mathematical object as exactly as I did
That's not why they are impossible you imbecile.
Post by Bassam Karzeddin
12) They would soon **REDISCOVER** suddenly that the compass is never a valid tool to make a circle, as exactly as I did
This is your claim, but not valid.
Post by Bassam Karzeddin
13) They would soon **REDISCOVER** suddenly that (0.999...) isn't a number and as exactly as I did in older posts beside few other members of sci. math as JG
Citing a infamous crank like Gabriel weakens your position, not strengthen.
A dipshit incurable academic troll and imbecile mathematiker Zelos is
Well-certified by many members as a Physico severe mental case who always bring the worst of maths he had blindly inherited
Can't get a hint yet to what is truly happening nowadays in mathematics on the top-levels with many references before his own eyes
He is certainly a hired troll who fails usually to convince anyone about anything of his old inherited false beliefs
If (7 - 3 - 4 = 0) is a deformed shape of an original natural numerical equation like this (7 = 3 + 4), and without zero and without negatives
So, where are your zero and negative Moron
It is the seventh impossible to correctly communicate only with such common academic mathematicians like Zelos about such a very fundamental issue
Who cares for your nonsense Moron?
You can't get any hint yet and you shouldn't for sure
My issues are not meant for your likes Zelos Malume Idiot
BKK
I do feel as though I am about as extreme as the 'standard' USENET (ab)user here on sci.math. But really I try to treat these topics as open. I ask that you who are unafraid to criticize likewise be unafraid to construct. This is a freedom that we all must grant ourselves, yet it is nothing like the burden of accountability as we sat in classrooms knowing that if we failed to mimic the presentation that we would be offed. As I read the lines of rejectional thinking here I can't help but expose the trap of academia.
4 - 3 =/= 3 - 4
and indeed the only time that symmetry can be had is when
+ 2 - 2 = 0 = - 2 + 2
Please Note something doubtful here about creating unnecessary illegal number like zero
Naturally, with significant integers or natural numbers (n), described as positive integers in standard mathematics, we have (n = n), which is a very meaningless equation, so like we have (2 = 2), without an unnecessary human brain fart
Then why the hell we should rewrite the same nonsense (2=2) into other larger nonsense like this (2 - 2 = 0), adding unnecessay the negative operation and a non-existing number like zero? wounders!
Yes, well, Descartes would agree with you possibly. Not for me to shove words in his mouth. I have a new reason. It is because the next stage of this progression yields:
- 2 + 2 * 2 = 0
and this form is new and different. Thank you Bassam for actually coming into some content here. It is greatly appreciated and as much as I can agree with you in some of your criticisms, and they are big, this open stance is ultimately the freedom to construct; our freedom to deconstruct as well. Is the one physics and the other mathematics? I think not.
Post by Bassam Karzeddin
And furher go to the negatives and create many illegal babies numbers like the imaginaries and more the complex numbers and further many more incomprehensible riddles arise the Raymond hypothesis and many more just because the older generations of mathematicians wanted to generate theorems that should benefit them only on the shoulders of all humans so illegally I must admit
In fact, most of the current mathematical riddles that are bothering the mathematicians for many centuries are purely fake and resulting from their own illegal thinking and they are entirely pure human mind cheat mainly for entertaining
Not to mention how bad that was reflected in many other theoretical sciences like the physics which uses such wrong concept in mathematics to come up suddenly with negative mass, the maximum speed of light, and soon the imaginary mass or energy and alike with many universes as well to a limit of adding so many legendary stories that any religion would be very ashamed of to include
Of course, there are truer and older mathematical puzzles that are strictly in number theory still standing for centuries and thousands of years as well
So, the best-alleged living mathematicians generally aren't aware of how harmful and too dangerous their own shallow and hollow thinking on the entire humanity as an inevitable result (where luckily for them, this is very away from any wide public attention in this century)
Regards
Bassam Karzeddin
Post by Timothy Golden
and strangely enough this is extremely near to polysign's own requirements. Now of course in these arithmetic systems there lays many an interpretation that ultimately are equivalent and hence a list of six or so formal constructions of the real number. I didn't really mean to go here so let's just put a 'todo' on this one. Possibly there is a more convincing route to polysign here though for me it seems indirect. That is irrelevant though; if it guides people into polysign then some criterion of value is had.
More to the point is that abstract algebra in some ways is a return to Descarte's false roots. But the signs are now in the values so subtraction is merely the addition of the inverse and all is well... except that we are free to develop interpretations on these goings on. The value of these interpretations can be meaningful if variations arise from their analysis. Just one minor fleck formalized could turn the math world to its knees. I know we all want to take it there. It is a hideous beast of snotty professors bordering on theologists. They are the perfect mimics. They are the problem. Obviously they didn't set out to be that way. Then too there are the journals... a level up in the hierarchy. Openness is not their strong suit. Criticism of the topic at hand or personal philosophy will not be put on the lectern, or if they are it will be done with great care so as not to upset their neighbors. We are the fortunate ones who arrive here in an uncensored space; who remain powerless; who are allowed to make mistakes!
Addition is integration is superpostion is fundamental. Multiplication is not so. It may mimic it and we may do it, but the fundamental sensibility of it is lost particularly within geometrical representations. The notion that
a b
exists in the same set as a and as b is not actually what we observe. Well then is this physics or is this mathematics? Of course I see that question as asinine. Is this philosophy or mathematics?
The sum is just
The product not so
And of the X many say much
zelos...@gmail.com
2020-11-06 06:53:33 UTC
Post by Timothy Golden
Post by Bassam Karzeddin
Post by Timothy Golden
Post by Bassam Karzeddin
Post by ***@gmail.com
Post by Bassam Karzeddin
Does it seem that recently, the anonymous professional mathematicians at *Donkeypedia** started again bounding their too lengthy business about what is a real number?
You hate wikipedia cause it shows you wrong.
Post by Bassam Karzeddin
Now they are recognizing that even the word positive doesn't have true meaning since it came after inventing the untrue negative numbers
Negative numbers can be constructed, get over it.
Post by Bassam Karzeddin
Look carefully how many older threads I wrote about it with full details and simple numerical examples
You have never demonstrated their non-existence because you cannot show a contradiction.
Post by Bassam Karzeddin
They are realizing now that negative and imaginary numbers are human mind fart numbers (as I exactly did in so many published threads before them)
All numbers are made in our minds.
Post by Bassam Karzeddin
1) They would soon **REDISCOVER** suddenly that the Cardano formula is quite **FALSE** as exactly as I did
Except it is demonstrably correct so tough shit.
Post by Bassam Karzeddin
2) They would soon **REDISCOVER** suddenly that (Galois, Ruffanee and Aple) the theorem is also **FALSE** as exactly as I did
except they are demonstrably true.
Post by Bassam Karzeddin
3) They would soon **REDISCOVER** suddenly that the endless act of (Dedikuned cuts, Cauchy sequences, Intermediate theorems, Limits, Convergence, ..., etc) can't define truly a single real existing (constructible) number), as exactly as I did
Except we can show that they do give real number structures so tough shit. You're wrong.
Post by Bassam Karzeddin
4) They would soon **REDISCOVER** suddenly that the vast majorities of the well-known angles in both old and modern mathematics don't even exist, as exactly as I did
Its all just real numbers so you are simply wrong here.
Post by Bassam Karzeddin
5) They would soon **REDISCOVER** suddenly that the true existing numbers are only those described in the standard mathematics as positive constructible numbers, as exactly as I did
Why would those be the only numbers? That is your idiotic idea, not mathematics.
Post by Bassam Karzeddin
6) They would soon **REDISCOVER** suddenly that the most worshipped human mind numbers (pi, e, 0 and the cube root of a prime number) aren't real nor existing numbers, as exactly as I did
Except we can construct all of them so tough shit.
Post by Bassam Karzeddin
7)They would soon **REDISCOVER** suddenly that the imaginary numbers were a very false decision as exactly as I did
Except its used and useful and we can easily construct it using |R[x]/<x^2+1> so exist it does.
8) They would soon **REDISCOVER** suddenly that continuity of real numbers don't exist and the real (constructible) numbers are discrete numbers, as exactly as I did
Even in rational numbers, it ain't discrete you moron.
Post by Bassam Karzeddin
9) They would soon **REDISCOVER** suddenly that the Euclidean space is the only true spaces were curved space or spacetime is a fart idea, as exactly as I did
Except we know space is curved both on earth adn the actual spacetime and euclidean cannot account or describe them so.
Post by Bassam Karzeddin
10) They would soon **REDISCOVER** suddenly that the Non-Euclidean geometry exists only in Euclidean geometry as exactly as I did
It is not in it cause they require statements that are false in euclidean you imbecile.
Post by Bassam Karzeddin
11) They would soon **REDISCOVER** suddenly that the true solution to the three impossible constructin problems raised by the ancient Greeks are impossible constructions by any tools or means since nither the circle nor the cube root two is an existing mathematical object as exactly as I did
That's not why they are impossible you imbecile.
Post by Bassam Karzeddin
12) They would soon **REDISCOVER** suddenly that the compass is never a valid tool to make a circle, as exactly as I did
This is your claim, but not valid.
Post by Bassam Karzeddin
13) They would soon **REDISCOVER** suddenly that (0.999...) isn't a number and as exactly as I did in older posts beside few other members of sci. math as JG
Citing a infamous crank like Gabriel weakens your position, not strengthen.
A dipshit incurable academic troll and imbecile mathematiker Zelos is
Well-certified by many members as a Physico severe mental case who always bring the worst of maths he had blindly inherited
Can't get a hint yet to what is truly happening nowadays in mathematics on the top-levels with many references before his own eyes
He is certainly a hired troll who fails usually to convince anyone about anything of his old inherited false beliefs
If (7 - 3 - 4 = 0) is a deformed shape of an original natural numerical equation like this (7 = 3 + 4), and without zero and without negatives
So, where are your zero and negative Moron
It is the seventh impossible to correctly communicate only with such common academic mathematicians like Zelos about such a very fundamental issue
Who cares for your nonsense Moron?
You can't get any hint yet and you shouldn't for sure
My issues are not meant for your likes Zelos Malume Idiot
BKK
I do feel as though I am about as extreme as the 'standard' USENET (ab)user here on sci.math. But really I try to treat these topics as open. I ask that you who are unafraid to criticize likewise be unafraid to construct. This is a freedom that we all must grant ourselves, yet it is nothing like the burden of accountability as we sat in classrooms knowing that if we failed to mimic the presentation that we would be offed. As I read the lines of rejectional thinking here I can't help but expose the trap of academia.
4 - 3 =/= 3 - 4
and indeed the only time that symmetry can be had is when
+ 2 - 2 = 0 = - 2 + 2
Please Note something doubtful here about creating unnecessary illegal number like zero
Naturally, with significant integers or natural numbers (n), described as positive integers in standard mathematics, we have (n = n), which is a very meaningless equation, so like we have (2 = 2), without an unnecessary human brain fart
Then why the hell we should rewrite the same nonsense (2=2) into other larger nonsense like this (2 - 2 = 0), adding unnecessay the negative operation and a non-existing number like zero? wounders!
- 2 + 2 * 2 = 0
and this form is new and different. Thank you Bassam for actually coming into some content here. It is greatly appreciated and as much as I can agree with you in some of your criticisms, and they are big, this open stance is ultimately the freedom to construct; our freedom to deconstruct as well. Is the one physics and the other mathematics? I think not.
Post by Bassam Karzeddin
And furher go to the negatives and create many illegal babies numbers like the imaginaries and more the complex numbers and further many more incomprehensible riddles arise the Raymond hypothesis and many more just because the older generations of mathematicians wanted to generate theorems that should benefit them only on the shoulders of all humans so illegally I must admit
In fact, most of the current mathematical riddles that are bothering the mathematicians for many centuries are purely fake and resulting from their own illegal thinking and they are entirely pure human mind cheat mainly for entertaining
Not to mention how bad that was reflected in many other theoretical sciences like the physics which uses such wrong concept in mathematics to come up suddenly with negative mass, the maximum speed of light, and soon the imaginary mass or energy and alike with many universes as well to a limit of adding so many legendary stories that any religion would be very ashamed of to include
Of course, there are truer and older mathematical puzzles that are strictly in number theory still standing for centuries and thousands of years as well
So, the best-alleged living mathematicians generally aren't aware of how harmful and too dangerous their own shallow and hollow thinking on the entire humanity as an inevitable result (where luckily for them, this is very away from any wide public attention in this century)
Regards
Bassam Karzeddin
Post by Timothy Golden
and strangely enough this is extremely near to polysign's own requirements. Now of course in these arithmetic systems there lays many an interpretation that ultimately are equivalent and hence a list of six or so formal constructions of the real number. I didn't really mean to go here so let's just put a 'todo' on this one. Possibly there is a more convincing route to polysign here though for me it seems indirect. That is irrelevant though; if it guides people into polysign then some criterion of value is had.
More to the point is that abstract algebra in some ways is a return to Descarte's false roots. But the signs are now in the values so subtraction is merely the addition of the inverse and all is well... except that we are free to develop interpretations on these goings on. The value of these interpretations can be meaningful if variations arise from their analysis. Just one minor fleck formalized could turn the math world to its knees. I know we all want to take it there. It is a hideous beast of snotty professors bordering on theologists. They are the perfect mimics. They are the problem. Obviously they didn't set out to be that way. Then too there are the journals... a level up in the hierarchy. Openness is not their strong suit. Criticism of the topic at hand or personal philosophy will not be put on the lectern, or if they are it will be done with great care so as not to upset their neighbors. We are the fortunate ones who arrive here in an uncensored space; who remain powerless; who are allowed to make mistakes!
Addition is integration is superpostion is fundamental. Multiplication is not so. It may mimic it and we may do it, but the fundamental sensibility of it is lost particularly within geometrical representations. The notion that
a b
exists in the same set as a and as b is not actually what we observe. Well then is this physics or is this mathematics? Of course I see that question as asinine. Is this philosophy or mathematics?
The sum is just
The product not so
And of the X many say much
why wont you answer my question?
Timothy Golden
2020-11-06 11:24:05 UTC
Post by ***@gmail.com
Post by Timothy Golden
Post by Bassam Karzeddin
Post by Timothy Golden
Post by Bassam Karzeddin
Post by ***@gmail.com
Post by Bassam Karzeddin
Does it seem that recently, the anonymous professional mathematicians at *Donkeypedia** started again bounding their too lengthy business about what is a real number?
You hate wikipedia cause it shows you wrong.
Post by Bassam Karzeddin
Now they are recognizing that even the word positive doesn't have true meaning since it came after inventing the untrue negative numbers
Negative numbers can be constructed, get over it.
Post by Bassam Karzeddin
Look carefully how many older threads I wrote about it with full details and simple numerical examples
You have never demonstrated their non-existence because you cannot show a contradiction.
Post by Bassam Karzeddin
They are realizing now that negative and imaginary numbers are human mind fart numbers (as I exactly did in so many published threads before them)
All numbers are made in our minds.
Post by Bassam Karzeddin
1) They would soon **REDISCOVER** suddenly that the Cardano formula is quite **FALSE** as exactly as I did
Except it is demonstrably correct so tough shit.
Post by Bassam Karzeddin
2) They would soon **REDISCOVER** suddenly that (Galois, Ruffanee and Aple) the theorem is also **FALSE** as exactly as I did
except they are demonstrably true.
Post by Bassam Karzeddin
3) They would soon **REDISCOVER** suddenly that the endless act of (Dedikuned cuts, Cauchy sequences, Intermediate theorems, Limits, Convergence, ..., etc) can't define truly a single real existing (constructible) number), as exactly as I did
Except we can show that they do give real number structures so tough shit. You're wrong.
Post by Bassam Karzeddin
4) They would soon **REDISCOVER** suddenly that the vast majorities of the well-known angles in both old and modern mathematics don't even exist, as exactly as I did
Its all just real numbers so you are simply wrong here.
Post by Bassam Karzeddin
5) They would soon **REDISCOVER** suddenly that the true existing numbers are only those described in the standard mathematics as positive constructible numbers, as exactly as I did
Why would those be the only numbers? That is your idiotic idea, not mathematics.
Post by Bassam Karzeddin
6) They would soon **REDISCOVER** suddenly that the most worshipped human mind numbers (pi, e, 0 and the cube root of a prime number) aren't real nor existing numbers, as exactly as I did
Except we can construct all of them so tough shit.
Post by Bassam Karzeddin
7)They would soon **REDISCOVER** suddenly that the imaginary numbers were a very false decision as exactly as I did
Except its used and useful and we can easily construct it using |R[x]/<x^2+1> so exist it does.
8) They would soon **REDISCOVER** suddenly that continuity of real numbers don't exist and the real (constructible) numbers are discrete numbers, as exactly as I did
Even in rational numbers, it ain't discrete you moron.
Post by Bassam Karzeddin
9) They would soon **REDISCOVER** suddenly that the Euclidean space is the only true spaces were curved space or spacetime is a fart idea, as exactly as I did
Except we know space is curved both on earth adn the actual spacetime and euclidean cannot account or describe them so.
Post by Bassam Karzeddin
10) They would soon **REDISCOVER** suddenly that the Non-Euclidean geometry exists only in Euclidean geometry as exactly as I did
It is not in it cause they require statements that are false in euclidean you imbecile.
Post by Bassam Karzeddin
11) They would soon **REDISCOVER** suddenly that the true solution to the three impossible constructin problems raised by the ancient Greeks are impossible constructions by any tools or means since nither the circle nor the cube root two is an existing mathematical object as exactly as I did
That's not why they are impossible you imbecile.
Post by Bassam Karzeddin
12) They would soon **REDISCOVER** suddenly that the compass is never a valid tool to make a circle, as exactly as I did
This is your claim, but not valid.
Post by Bassam Karzeddin
13) They would soon **REDISCOVER** suddenly that (0.999...) isn't a number and as exactly as I did in older posts beside few other members of sci. math as JG
Citing a infamous crank like Gabriel weakens your position, not strengthen.
A dipshit incurable academic troll and imbecile mathematiker Zelos is
Well-certified by many members as a Physico severe mental case who always bring the worst of maths he had blindly inherited
Can't get a hint yet to what is truly happening nowadays in mathematics on the top-levels with many references before his own eyes
He is certainly a hired troll who fails usually to convince anyone about anything of his old inherited false beliefs
If (7 - 3 - 4 = 0) is a deformed shape of an original natural numerical equation like this (7 = 3 + 4), and without zero and without negatives
So, where are your zero and negative Moron
It is the seventh impossible to correctly communicate only with such common academic mathematicians like Zelos about such a very fundamental issue
Who cares for your nonsense Moron?
You can't get any hint yet and you shouldn't for sure
My issues are not meant for your likes Zelos Malume Idiot
BKK
I do feel as though I am about as extreme as the 'standard' USENET (ab)user here on sci.math. But really I try to treat these topics as open. I ask that you who are unafraid to criticize likewise be unafraid to construct. This is a freedom that we all must grant ourselves, yet it is nothing like the burden of accountability as we sat in classrooms knowing that if we failed to mimic the presentation that we would be offed. As I read the lines of rejectional thinking here I can't help but expose the trap of academia.
4 - 3 =/= 3 - 4
and indeed the only time that symmetry can be had is when
+ 2 - 2 = 0 = - 2 + 2
Please Note something doubtful here about creating unnecessary illegal number like zero
Naturally, with significant integers or natural numbers (n), described as positive integers in standard mathematics, we have (n = n), which is a very meaningless equation, so like we have (2 = 2), without an unnecessary human brain fart
Then why the hell we should rewrite the same nonsense (2=2) into other larger nonsense like this (2 - 2 = 0), adding unnecessay the negative operation and a non-existing number like zero? wounders!
- 2 + 2 * 2 = 0
and this form is new and different. Thank you Bassam for actually coming into some content here. It is greatly appreciated and as much as I can agree with you in some of your criticisms, and they are big, this open stance is ultimately the freedom to construct; our freedom to deconstruct as well. Is the one physics and the other mathematics? I think not.
Post by Bassam Karzeddin
And furher go to the negatives and create many illegal babies numbers like the imaginaries and more the complex numbers and further many more incomprehensible riddles arise the Raymond hypothesis and many more just because the older generations of mathematicians wanted to generate theorems that should benefit them only on the shoulders of all humans so illegally I must admit
In fact, most of the current mathematical riddles that are bothering the mathematicians for many centuries are purely fake and resulting from their own illegal thinking and they are entirely pure human mind cheat mainly for entertaining
Not to mention how bad that was reflected in many other theoretical sciences like the physics which uses such wrong concept in mathematics to come up suddenly with negative mass, the maximum speed of light, and soon the imaginary mass or energy and alike with many universes as well to a limit of adding so many legendary stories that any religion would be very ashamed of to include
Of course, there are truer and older mathematical puzzles that are strictly in number theory still standing for centuries and thousands of years as well
So, the best-alleged living mathematicians generally aren't aware of how harmful and too dangerous their own shallow and hollow thinking on the entire humanity as an inevitable result (where luckily for them, this is very away from any wide public attention in this century)
Regards
Bassam Karzeddin
Post by Timothy Golden
and strangely enough this is extremely near to polysign's own requirements. Now of course in these arithmetic systems there lays many an interpretation that ultimately are equivalent and hence a list of six or so formal constructions of the real number. I didn't really mean to go here so let's just put a 'todo' on this one. Possibly there is a more convincing route to polysign here though for me it seems indirect. That is irrelevant though; if it guides people into polysign then some criterion of value is had.
More to the point is that abstract algebra in some ways is a return to Descarte's false roots. But the signs are now in the values so subtraction is merely the addition of the inverse and all is well... except that we are free to develop interpretations on these goings on. The value of these interpretations can be meaningful if variations arise from their analysis. Just one minor fleck formalized could turn the math world to its knees. I know we all want to take it there. It is a hideous beast of snotty professors bordering on theologists. They are the perfect mimics. They are the problem. Obviously they didn't set out to be that way. Then too there are the journals... a level up in the hierarchy. Openness is not their strong suit. Criticism of the topic at hand or personal philosophy will not be put on the lectern, or if they are it will be done with great care so as not to upset their neighbors. We are the fortunate ones who arrive here in an uncensored space; who remain powerless; who are allowed to make mistakes!
Addition is integration is superpostion is fundamental. Multiplication is not so. It may mimic it and we may do it, but the fundamental sensibility of it is lost particularly within geometrical representations. The notion that
a b
exists in the same set as a and as b is not actually what we observe. Well then is this physics or is this mathematics? Of course I see that question as asinine. Is this philosophy or mathematics?
The sum is just
The product not so
And of the X many say much
why wont you answer my question?
You say: "again mate, read the formal definition. There is no sum, it is only historic notation. "
and this is a fine resting place. You have denied the sum; distanced yourself thoroughly from the polynomial form; and in effect supported my own argument: https://groups.google.com/g/sci.math/c/yGQpEVY7n2c/m/5hzqN1A-AgAJ

I do understand the workings of the polynomial form from without where there are just a few creaks and groans, but when we dismantle the polynomial the alarm bells start ringing.

You yourself are support for the mantra:
The sum is not a sum
The product not a product
X is nothing at all

At least we see where the first line comes from. Zelos if you'd like to engage in the problem which certainly is wiped away by the ordered series form and in fact explains the need to transition over to that form then the context is not one of refutation here. The subject is weak and you help expose it this way. As far as I can tell we are in agreement while you deny the existence of any trouble. The incoherence is all yours. That said I will have to admit that I am fully capable of drawing incoherent conclusions as well, but by owning them and moving on hopefully we travel into a space of greater integrity. I am trying to rise above the fray these days and treat the problems as open. I encourage you to join me in this pursuit. I do believe that the sum is just whereas you accept a fault and bury the fact. This is the actual difference between us. I am more of the ring than you are. That a curriculum could cheat and then persecute its students under the guise of purity is a fraud and a sham my man. That you are being biblical here; I can't quite cleanly accuse you of this because you have come thus far as to admit that under the ring requirement the sum that I witness in
a0 + a1 X
is not a sum. Now if we could just get you to utter the next part on the product:
1.23 X
then we will be two thirds of the way to a full win. As for the pesky X that lacks any defining elemental status, well, that is just set theory right? As for the dimensional analysis of the situation you might say: what analysis? what dimension are you talking about? we never mentioned anything about dimension. How dare you?

Please come Zelos: do not be my whipping boy. Rise above the frayed end. Those will hopefully burn off and we will find some fresh material to work from. The singed material will simply fall to the earth and no longer be a hindrance. Then you will feel the lash fully. Ha Ha Ha!
zelos...@gmail.com
2020-11-06 12:37:34 UTC
Post by Timothy Golden
You have denied the sum
If the definition has no sum, it isn't a sum.
Post by Timothy Golden
distanced yourself thoroughly from the polynomial form
Not at all, because we are talking about polynomials, which has their formal definition and construction. It is not based on notation.
Post by Timothy Golden
I do understand the workings of the polynomial form from without where there are just a few creaks and groans, but when we dismantle the polynomial the alarm bells start ringing
Yet you do not undrstand that you use the formal definition to make complaints, not based on notation.
Post by Timothy Golden
You yourself are support for the mantra
Notation does not make something.
Post by Timothy Golden
The subject is weak and you help expose it this way. As far as I can tell we are in agreement while you deny the existence of any trouble
You have not pointed out any trouble that isn't based on notation by you. I challange you to find the issue you talk about while using the formal definition, not notation.
Post by Timothy Golden
The incoherence is all yours
Me? I use the formal definition, you complain about notation and never bother with the formal construction!.
Post by Timothy Golden
I do believe that the sum is just whereas you accept a fault and bury the fact
What fault? THere is no fault because in the formal definition there is no sum or the likes that you complain about!
Post by Timothy Golden
That a curriculum could cheat and then persecute its students under the guise of purity is a fraud and a sham my man
They don't cheat because there is an understanding by that level that notation does not make something, it is just symbols in a string.
Post by Timothy Golden
That you are being biblical here; I can't quite cleanly accuse you of this because you have come thus far as to admit that under the ring requirement the sum that I witness in
Exactly, ALL you do is focus on NOTATION, what we write. You don't focus on WHAT IT IS!
Post by Timothy Golden
a0 + a1 X
is notation for (a_0,a_1,0,0,0,...) when we use the |R^|N construction, but that doesn't mean that in the actual object, as I gave here in proper notation, has any sum or product in it.
Post by Timothy Golden
As for the pesky X that lacks any defining elemental status, well, that is just set theory right?
because they are notation, not actual objects. The exponent on X tells which n for f e |R^|N gives the real number before. Again, you complain about notation, not the fucking object/ring itself.
Post by Timothy Golden
Please come Zelos: do not be my whipping boy.
I am not because I know more mathematics than you, I am the one showing you as stupid :)
Post by Timothy Golden
Rise above the frayed end.
Can you go beyond highschool and understand that notation is not the object.

Can you learn this?
Peter
2020-11-06 18:14:23 UTC
[...] come thus far as to admit that under the ring requirement the sum that
I witness in
a0 + a1 X
1.23 X
then [...]
A polynomial (I claim) is (in the case that interests you) a sequence
s_0, s_1, s_2, ... of real numbers subject to only finitely many of them
being not zero. The set of such sequences can be furnished with a sum
and a product so as to make it a ring. In that case

a0 + a1 X

is the sum of these sequences

a0, 0, 0, 0, ... and 0, a1, 0, ...;

and

1.23 X

is the product of these sequences

1.23, 0, 0, ... and 0, 1, 0, 0, ...

Comments on my two parenthetical remarks:
"I claim" - and many algebra texts claim it too. My guess is that you
have never read an algebra text, and you will never do so.
"in the case that interests you" - polynomial are eventually zero
sequences of elements of a ring. The real numbers constitute a ring.
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
Timothy Golden
2020-11-14 13:27:40 UTC
Post by Timothy Golden
[...] come thus far as to admit that under the ring requirement the sum that
I witness in
a0 + a1 X
1.23 X
then [...]
A polynomial (I claim) is (in the case that interests you) a sequence
s_0, s_1, s_2, ... of real numbers subject to only finitely many of them
being not zero. The set of such sequences can be furnished with a sum
and a product so as to make it a ring. In that case
a0 + a1 X
is the sum of these sequences
a0, 0, 0, 0, ... and 0, a1, 0, ...;
and
1.23 X
is the product of these sequences
1.23, 0, 0, ... and 0, 1, 0, 0, ...
"I claim" - and many algebra texts claim it too. My guess is that you
have never read an algebra text, and you will never do so.
"in the case that interests you" - polynomial are eventually zero
sequences of elements of a ring. The real numbers constitute a ring.
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
Oh, so http://abstract.ups.edu/aata/section-poly-rings.html
is totally wrong, eh?

As far as I am concerned the dodge over to the ordered series is support for my own argument. It means that you do see the problem and that you resolve it by sweeping it under a carpet. That the two notations are supposed to be exactly equivalent means nothing to you. I actually agree that they are not equivalent, but further that the tax laid on insisting on an infinite dimensional construct almost all of whose elements are value zero is the most ridiculous corner to cower in. I must point you in a direction more appropriate to your own style of thinking: "6. It is not the function of the Ethics Committee to decide the authenticity of any item. If any dispute concerns the question of authenticity, the complainant must provide sufficient proof to the Ethics Committee that the item in question is not authentic and that such proof has been brought to the attention of the other party involved in the dispute." - https://www.wag-society.org/ethics.php
Peter
2020-11-14 15:57:17 UTC
Post by Timothy Golden
Post by Timothy Golden
[...] come thus far as to admit that under the ring requirement the sum that
I witness in
a0 + a1 X
1.23 X
then [...]
A polynomial (I claim) is (in the case that interests you) a sequence
s_0, s_1, s_2, ... of real numbers subject to only finitely many of them
being not zero. The set of such sequences can be furnished with a sum
and a product so as to make it a ring. In that case
a0 + a1 X
is the sum of these sequences
a0, 0, 0, 0, ... and 0, a1, 0, ...;
and
1.23 X
is the product of these sequences
1.23, 0, 0, ... and 0, 1, 0, 0, ...
"I claim" - and many algebra texts claim it too. My guess is that you
have never read an algebra text, and you will never do so.
"in the case that interests you" - polynomial are eventually zero
sequences of elements of a ring. The real numbers constitute a ring.
Oh, so http://abstract.ups.edu/aata/section-poly-rings.html
is totally wrong, eh?
No, I see nothing wrong with it. It does show that you are wrong though.
Post by Timothy Golden
As far as I am concerned the dodge over to the ordered series is support for my own argument. It means that you do see the problem and that you resolve it by sweeping it under a carpet. That the two notations are supposed to be exactly equivalent means nothing to you. I actually agree that they are not equivalent
Who are you agreeing with? They are equivalent
Post by Timothy Golden
, but further that the tax laid on insisting on an infinite dimensional construct almost all of whose elements are value zero is the most ridiculous corner to cower in. I must point you in a direction more appropriate to your own style of thinking: "6. It is not the function of the Ethics Committee to decide the authenticity of any item. If any dispute concerns the question of authenticity, the complainant must provide sufficient proof to the Ethics Committee that the item in question is not authentic and that such proof has been brought to the attention of the other party involved in the dispute." - https://www.wag-society.org/ethics.php
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
Peter
2020-11-16 15:22:16 UTC
Post by Timothy Golden
Post by Timothy Golden
[...] come thus far as to admit that under the ring requirement the sum that
I witness in
a0 + a1 X
1.23 X
then [...]
A polynomial (I claim) is (in the case that interests you) a sequence
s_0, s_1, s_2, ... of real numbers subject to only finitely many of them
being not zero. The set of such sequences can be furnished with a sum
and a product so as to make it a ring. In that case
a0 + a1 X
is the sum of these sequences
a0, 0, 0, 0, ... and 0, a1, 0, ...;
and
1.23 X
is the product of these sequences
1.23, 0, 0, ... and 0, 1, 0, 0, ...
"I claim" - and many algebra texts claim it too. My guess is that you
have never read an algebra text, and you will never do so.
"in the case that interests you" - polynomial are eventually zero
sequences of elements of a ring. The real numbers constitute a ring.
Oh, so http://abstract.ups.edu/aata/section-poly-rings.html
is totally wrong, eh?
No, I see nothing wrong with it.  It does show that you are wrong though.
Post by Timothy Golden
As far as I am concerned the dodge over to the ordered series is
support for my own argument. It means that you do see the problem and
that you resolve it by sweeping it under a carpet. That the two
notations are supposed to be exactly equivalent means nothing to you.
I actually agree that they are not equivalent
Who are you agreeing with?  They are equivalent
That the map which carries a_0, a_1, a_2, 0, 0, ... to
a_0 + a_1 X + a_2 X^2 is an isomorphism is obvious. I recognize that
you don't see that it's an isomorphism because you don't know what an
isomorphism is.
Post by Timothy Golden
, but further that the tax laid on insisting on an infinite
dimensional construct almost all of whose elements are value zero is
the most ridiculous corner to cower in. I must point you in a
direction more appropriate to your own style of thinking: "6. It is
not the function of the Ethics Committee to decide the authenticity of
any item. If any dispute concerns the question of authenticity, the
complainant must provide sufficient proof to the Ethics Committee that
the item in question is not authentic and that such proof has been
brought to the attention of the other party involved in the dispute."
- https://www.wag-society.org/ethics.php
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
zelos...@gmail.com
2020-11-16 06:22:37 UTC
Post by Timothy Golden
Post by Timothy Golden
[...] come thus far as to admit that under the ring requirement the sum that
I witness in
a0 + a1 X
1.23 X
then [...]
A polynomial (I claim) is (in the case that interests you) a sequence
s_0, s_1, s_2, ... of real numbers subject to only finitely many of them
being not zero. The set of such sequences can be furnished with a sum
and a product so as to make it a ring. In that case
a0 + a1 X
is the sum of these sequences
a0, 0, 0, 0, ... and 0, a1, 0, ...;
and
1.23 X
is the product of these sequences
1.23, 0, 0, ... and 0, 1, 0, 0, ...
"I claim" - and many algebra texts claim it too. My guess is that you
have never read an algebra text, and you will never do so.
"in the case that interests you" - polynomial are eventually zero
sequences of elements of a ring. The real numbers constitute a ring.
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
Oh, so http://abstract.ups.edu/aata/section-poly-rings.html
is totally wrong, eh?
As far as I am concerned the dodge over to the ordered series is support for my own argument. It means that you do see the problem and that you resolve it by sweeping it under a carpet. That the two notations are supposed to be exactly equivalent means nothing to you. I actually agree that they are not equivalent, but further that the tax laid on insisting on an infinite dimensional construct almost all of whose elements are value zero is the most ridiculous corner to cower in. I must point you in a direction more appropriate to your own style of thinking: "6. It is not the function of the Ethics Committee to decide the authenticity of any item. If any dispute concerns the question of authenticity, the complainant must provide sufficient proof to the Ethics Committee that the item in question is not authentic and that such proof has been brought to the attention of the other party involved in the dispute." - https://www.wag-society.org/ethics.php
oh look, didn't address anything I pointed out
Timothy Golden
2020-11-16 15:11:56 UTC
Post by ***@gmail.com
Post by Timothy Golden
Post by Timothy Golden
[...] come thus far as to admit that under the ring requirement the sum that
I witness in
a0 + a1 X
1.23 X
then [...]
A polynomial (I claim) is (in the case that interests you) a sequence
s_0, s_1, s_2, ... of real numbers subject to only finitely many of them
being not zero. The set of such sequences can be furnished with a sum
and a product so as to make it a ring. In that case
a0 + a1 X
is the sum of these sequences
a0, 0, 0, 0, ... and 0, a1, 0, ...;
and
1.23 X
is the product of these sequences
1.23, 0, 0, ... and 0, 1, 0, 0, ...
"I claim" - and many algebra texts claim it too. My guess is that you
have never read an algebra text, and you will never do so.
"in the case that interests you" - polynomial are eventually zero
sequences of elements of a ring. The real numbers constitute a ring.
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
Oh, so http://abstract.ups.edu/aata/section-poly-rings.html
is totally wrong, eh?
As far as I am concerned the dodge over to the ordered series is support for my own argument. It means that you do see the problem and that you resolve it by sweeping it under a carpet. That the two notations are supposed to be exactly equivalent means nothing to you. I actually agree that they are not equivalent, but further that the tax laid on insisting on an infinite dimensional construct almost all of whose elements are value zero is the most ridiculous corner to cower in. I must point you in a direction more appropriate to your own style of thinking: "6. It is not the function of the Ethics Committee to decide the authenticity of any item. If any dispute concerns the question of authenticity, the complainant must provide sufficient proof to the Ethics Committee that the item in question is not authentic and that such proof has been brought to the attention of the other party involved in the dispute." - https://www.wag-society.org/ethics.php
oh look, didn't address anything I pointed out
Zelos you yourself have denied that the sum in the polynomial sum is a sum in order to rectify my criticism. I have no idea how you can go along with your insistence here. The chasm that you have built is not exactly your own: it is the result of a system of mimicry. What exactly did we buy into under threat of failure? Mimicry is not taking you along a path or a progression. Rather than land in the same drivel repetitively we need to cover more ground. There is no such from your side. Your own behavior is that of a bot. Can't you come up with any variation? Restate the problem even? I may not like your restatement and will likely criticize it in some way, but at least that would be a variation. I do hope they will install AGI 3 into you soon. I will happily communicate with bots and droids but I will insist upon interpretation and variation.
zelos...@gmail.com
2020-11-17 06:26:50 UTC
Post by Timothy Golden
Zelos you yourself have denied that the sum in the polynomial sum is a sum in order to rectify my criticism
I am telling you that it is ONLY NOTATION.

There IS no sum even if it is WRITTEN as such. How hard is it to understand that NOTATION is not whatd ecides things.
Post by Timothy Golden
I have no idea how you can go along with your insistence here
What inconsistency? I am very consistent in that I am telling you there is a HUGE differens between NOTATION and the object itself.
Post by Timothy Golden
I will happily communicate with bots and droids but I will insist upon interpretation and variation.
What are you on about? THere are no bots here, except maybe Archie
Timothy Golden
2020-11-17 19:11:13 UTC
Post by ***@gmail.com
Post by Timothy Golden
Zelos you yourself have denied that the sum in the polynomial sum is a sum in order to rectify my criticism
I am telling you that it is ONLY NOTATION.
There IS no sum even if it is WRITTEN as such. How hard is it to understand that NOTATION is not whatd ecides things.
Post by Timothy Golden
I have no idea how you can go along with your insistence here
What inconsistency? I am very consistent in that I am telling you there is a HUGE differens between NOTATION and the object itself.
Post by Timothy Golden
I will happily communicate with bots and droids but I will insist upon interpretation and variation.
What are you on about? THere are no bots here, except maybe Archie
Alright Zelos. I will accept your position as authentic and certainly you have held to it for a good long time. I do find it unfortunate in a subject which only just formalized the operators of sum and product to have such a discrepancy built into its productive (as in gaining results) form. To state that this is merely notation I cannot find acceptable, for it is this sum and product which allow for the greater behaviors of the polynomial format. We do in fact see the sum take form in many places such as the integral, the sigma notation, path dynamics, and the polynomial format. even our large number numerical notation implies a sum of terms in the radix of the system; a native power series if you will. That these power series get reuse across many places is significant. That we should construct them freely and without the ambiguity exposed in AA is rather a must I would say.

For instance the Mandelbrot iterated function of z[0]
z[n+1] = z[n] z[n] + z[0]
z1 = z0 z0 + z0
z2 = z1 z1 + z0 = (z0 z0 + z0 ) (z0 z0 + z0 ) + z0
z3 = z2 z2 + z0 = ((z0 z0 + z0 ) (z0 z0 + z0 ) + z0 ) ((z0 z0 + z0 ) (z0 z0 + z0 ) + z0) + z0
z4 = z3 z3 + z0 = (((z0 z0 + z0 ) (z0 z0 + z0 ) + z0 ) ((z0 z0 + z0 ) (z0 z0 + z0 ) + z0) + z0 ) (((z0 z0 + z0 ) (z0 z0 + z0 ) + z0 ) ((z0 z0 + z0 ) (z0 z0 + z0 ) + z0) + z0) + z0
z5 = z4 z4 + z0 = ( (((z0 z0 + z0 ) (z0 z0 + z0 ) + z0 ) ((z0 z0 + z0 ) (z0 z0 + z0 ) + z0) + z0 ) (((z0 z0 + z0 ) (z0 z0 + z0 ) + z0 ) ((z0 z0 + z0 ) (z0 z0 + z0 ) + z0) + z0) + z0 ) ( (((z0 z0 + z0 ) (z0 z0 + z0 ) + z0 ) ((z0 z0 + z0 ) (z0 z0 + z0 ) + z0) + z0 ) (((z0 z0 + z0 ) (z0 z0 + z0 ) + z0 ) ((z0 z0 + z0 ) (z0 z0 + z0 ) + z0) + z0) + z0) + z0
...

Now distributing terms... Hah. Won't be doing that anytime soon. Maybe when I master sage math I will get it to do the dirty work.
You see Zelos when you give up the sum or the product you are giving up on factoring your polynomial. Your defense is a no go. It is not absolutely necessary to retain factorization to get some results, but to toss that option out the window to dodge a dirty secret swept under the carpet where a low spot has allowed a puddle of mud to form; it's not good. AA is not good. I can say with certainty that it is not good with me. It is good with you and that is fine. I can respect your person though you better take while you can. As for the belief, well, I have confronted it here aplenty. That is all that I can do.

We are all fools. We are all tools of the system. Still, when Shakespeare's monkeys run amuck en masse then the trap is sprung. I will try to find a way out for you. For now though you are in there with a black swan that is not so friendly and the cause of it all:
1.23 X
ah, but did you judge this product to not be a product? Or is your interpretation that you can hold onto closure here? You really do keep dodging the black swan. Not any more you dirty whore. Speak up on the product you wimp. You are a shrimp who cannot come to the table here and address this problem. We are going to see you two thirds of the way through:
The sum is not a sum.
The product not a product.
And that X is nothing at all.
zelos...@gmail.com
2020-11-18 06:31:41 UTC
Post by Timothy Golden
I do find it unfortunate in a subject which only just formalized the operators of sum and product to have such a discrepancy built into its productive (as in gaining results) form
Again if you argue based on notation you've failed from the beginning because the formal construction has none of those you complain about and IT is ALL that matters.
Post by Timothy Golden
To state that this is merely notation I cannot find acceptable,
If it is just notation then it is just notation and nothing else. A strnig of symbols to symbolize something. A is not the sound, it is a symbol to represent the sound.
Post by Timothy Golden
for it is this sum and product which allow for the greater behaviors of the polynomial format.
Not in the written one. The behavior of polynomials comes from its construction, not the notation.
Post by Timothy Golden
We do in fact see the sum take form in many places such as the integral
Integrals are not sums either :) Try again.
Post by Timothy Golden
the sigma notation
Sigma notation denotes sum generally.
Post by Timothy Golden
You see Zelos when you give up the sum or the product you are giving up on factoring your polynomial
not at all, 6 is neither a product nor a sum, it is a symbol for a number, but we can write 2*3=6

same way, if we haev (-1,0,1,0,0...) as the polynomial, I can write (-1,0,1,0,0...)=(-1,1,0,0,0...)*(1,1,0,0,0...)

so it works just fine without sum/product notation that you so focus on :)
Post by Timothy Golden
certainty that it is not good with me
What is good with you is irrelevant. Again if you cannot show that the FORMAL CONSTRUCTION is an actual sum (which it isn't) then your complains about sum/product when written is null and void.
Post by Timothy Golden
ah, but did you judge this product to not be a product?
It is notation for (0,1.23,0,0,0,...) is this too difficult to understand for you?
Post by Timothy Golden
Or is your interpretation that you can hold onto closure here?
Given it is notation for a sequence where almost all values are 0, yes it is entirely closed as a ring because all polynomials in formal construction are sequences where almost all values are 0.
Post by Timothy Golden
You really do keep dodging the black swan.
I have enver dodged anything, I have pointed out you are wrong from the get go assuming that notational product = actual product.
Oh the pain to my ego! If you are gonna go like this, maybe you should do proper mathematics and actually discuss formal definitions instead of colloquial understandings?

You are an intellectual midget by comparison :) Let's use the formal definition and continue the discussion, agreed?
Timothy Golden
2020-11-18 13:38:43 UTC
Post by ***@gmail.com
Post by Timothy Golden
I do find it unfortunate in a subject which only just formalized the operators of sum and product to have such a discrepancy built into its productive (as in gaining results) form
Again if you argue based on notation you've failed from the beginning because the formal construction has none of those you complain about and IT is ALL that matters.
Post by Timothy Golden
To state that this is merely notation I cannot find acceptable,
If it is just notation then it is just notation and nothing else. A strnig of symbols to symbolize something. A is not the sound, it is a symbol to represent the sound.
Post by Timothy Golden
for it is this sum and product which allow for the greater behaviors of the polynomial format.
Not in the written one. The behavior of polynomials comes from its construction, not the notation.
Post by Timothy Golden
We do in fact see the sum take form in many places such as the integral
Integrals are not sums either :) Try again.
Post by Timothy Golden
the sigma notation
Sigma notation denotes sum generally.
Post by Timothy Golden
You see Zelos when you give up the sum or the product you are giving up on factoring your polynomial
not at all, 6 is neither a product nor a sum, it is a symbol for a number, but we can write 2*3=6
same way, if we haev (-1,0,1,0,0...) as the polynomial, I can write (-1,0,1,0,0...)=(-1,1,0,0,0...)*(1,1,0,0,0...)
so it works just fine without sum/product notation that you so focus on :)
Post by Timothy Golden
certainty that it is not good with me
What is good with you is irrelevant. Again if you cannot show that the FORMAL CONSTRUCTION is an actual sum (which it isn't) then your complains about sum/product when written is null and void.
Post by Timothy Golden
ah, but did you judge this product to not be a product?
It is notation for (0,1.23,0,0,0,...) is this too difficult to understand for you?
Post by Timothy Golden
Or is your interpretation that you can hold onto closure here?
Given it is notation for a sequence where almost all values are 0, yes it is entirely closed as a ring because all polynomials in formal construction are sequences where almost all values are 0.
Post by Timothy Golden
You really do keep dodging the black swan.
I have enver dodged anything, I have pointed out you are wrong from the get go assuming that notational product = actual product.
Oh the pain to my ego! If you are gonna go like this, maybe you should do proper mathematics and actually discuss formal definitions instead of colloquial understandings?
You are an intellectual midget by comparison :) Let's use the formal definition and continue the discussion, agreed?
Fascinating. You really are holding to that singular argument. Again I credit you with persistence. I suppose I am forced at this point to insist upon the exact equivalence between the ordinary polynomial form and the ordered series notation. There is no magic wand present as you Mr. Z. Wiz. would have it. Here for instance is a text in use at MIT in modernity which does not disabuse the polynomial format:
http://abstract.ups.edu/aata/section-poly-rings.html
https://ocw.mit.edu/courses/mathematics/18-703-modern-algebra-spring-2013/related-resources/
Would you care to cite a work which does in fact disabuse the ordinary polynomial format? If you cannot find one which insists that the format is old and endangered as you so readily admit, then where does this leave your own argument?

Again, I find your own stance to be agreeable to mine; it's just that we are yielding starkly different conclusions. As to who is running a status quo campaign here and who is the underdog in this fight... your own misstep legitimates my very concern. In following this train of thought and returning again to the black swan whose singular operator is known to be a product:
1.23 X
where 1.23 is a real value and X is not a real value and so this product offends the closure requirement of the ring definition and thus all expressions composed with such a product must offend the ring definition and so all polynomials with real coefficients offend the ring definition. And yet the subject completely hinges and relies upon the claim that these polynomials are ring behaved.

Thus it is for you who utters that the sum is not a sum in
a0 + a1 X
to utter that the product is not a product in
a1 X
and of course then too we will be left to discuss nothing at all about the X.

It is already enough for me that you deny the sum. It is already enough for me that you deny the polynomial form. It is only for me to push you harder onto the bleeding edge here. Sources please Zelos. I have gotten one for you here. Now you get one for me here. And why would it be that the polynomial form has to go away? It can only be for exactly the reasons that I expose to the public here and that get swept under the carpet by you here. AA is as fraudulent a topic as you are a debater. Still in a moment of egalitarianism I must credit you for staying on here, but you must see how weak your own position is. I will try to remain open and accept your seriousness as well. It is possible that the empire can strike back. If it does so in lies that it believes authentically in, and this is the position of all who are mistaken, then so can I do the same. Let us run our truth saber through this material please.
Peter
2020-11-18 14:50:24 UTC
Post by Timothy Golden
Thus it is for you who utters that the sum is not a sum in
a0 + a1 X
to utter that the product is not a product in
a1 X
and of course then too we will be left to discuss nothing at all about the X.
Let R be a proper subring of a ring R'. Let x be a member of R' not in
R. A finite expression a_0 + a_1 X + a_2 X^2 +... has members a_0,
a_1,... in R. The whole thing is a member of R'. The sums are sums and
the products are products. This approach to polynomials will be found
in volume I of van der Waerden.
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
Timothy Golden
2020-11-20 16:00:20 UTC
Post by Timothy Golden
Thus it is for you who utters that the sum is not a sum in
a0 + a1 X
to utter that the product is not a product in
a1 X
and of course then too we will be left to discuss nothing at all about the X.
Let R be a proper subring of a ring R'. Let x be a member of R' not in
R. A finite expression a_0 + a_1 X + a_2 X^2 +... has members a_0,
a_1,... in R. The whole thing is a member of R'. The sums are sums and
the products are products. This approach to polynomials will be found
in volume I of van der Waerden.
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
But Peter is it clean? Isn't this essentially unioning X with the reals in the case of polynomials with real coefficients?
It won't work out. It already offends the ring requirements. I simply put before you again the black swan
1.23 X
which is not to evaluate to a single element in your new set. Please name this element for me. I think in your terseness you do see the problem. Possibly van der Waerden avoids the closure requirement in his build. It sure would be helpful to have an electronic link to the text you are using.
Do you have a title or ISBN or something like that?

Thank you Peter for staying on here. Was it you who got trapped in the cage with the black swan? I can't remember if it bit you or somebody else. The thing can be really vicious especially when you stare it in the face. It is not going to go away any time soon. If you could behead the thing I'd say have at it. But you've tried and tried as others here have. You land in sum in a mantra:
The sum is not a sum.
The product not a product.
And the X is nothing at all.
FromTheRafters
2020-11-20 16:30:26 UTC
Post by Timothy Golden
Post by Timothy Golden
Thus it is for you who utters that the sum is not a sum in
a0 + a1 X
to utter that the product is not a product in
a1 X
and of course then too we will be left to discuss nothing at all about the X.
Let R be a proper subring of a ring R'. Let x be a member of R' not in
R. A finite expression a_0 + a_1 X + a_2 X^2 +... has members a_0,
a_1,... in R. The whole thing is a member of R'. The sums are sums and
the products are products. This approach to polynomials will be found
in volume I of van der Waerden.
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
But Peter is it clean? Isn't this essentially unioning X with the reals in
the case of polynomials with real coefficients? It won't work out. It already
offends the ring requirements.
It has been asked before, but I don't recall there being an answer.
What exactly is it that you believe is "not ring behaved" or "offends
the ring requirements"?
Peter
2020-11-20 16:41:12 UTC
Post by Timothy Golden
Post by Timothy Golden
Thus it is for you who utters that the sum is not a sum in
a0 + a1 X
to utter that the product is not a product in
a1 X
and of course then too we will be left to discuss nothing at all about the X.
Let R be a proper subring of a ring R'. Let x be a member of R' not in
R. A finite expression a_0 + a_1 X + a_2 X^2 +... has members a_0,
a_1,... in R. The whole thing is a member of R'. The sums are sums and
the products are products. This approach to polynomials will be found
in volume I of van der Waerden.
But Peter is it clean? Isn't this essentially unioning X with the reals in the case of polynomials with real coefficients?
It won't work out
I doubt that you've every worked anything out. It's standard first year
stuff to show that if R is a ring then R[X] (however defined) is also a
ring.
Post by Timothy Golden
. It already offends the ring requirements. I simply put before you again the black swan
1.23 X
which is not to evaluate to a single element in your new set
It's very obviously an element of R'.
Post by Timothy Golden
. Please name this element for me.
Penelope? Frederick?
Post by Timothy Golden
I think in your terseness you do see the problem. Possibly van der Waerden avoids the closure requirement in his build
That's an idiotic suggestion.
Post by Timothy Golden
. It sure would be helpful to have an electronic link to the text you are using.
Do you have a title or ISBN or something like that?
The sum is not a sum.
The product not a product.
And the X is nothing at all.
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
Timothy Golden
2020-11-20 23:19:10 UTC
Post by Timothy Golden
Post by Timothy Golden
Thus it is for you who utters that the sum is not a sum in
a0 + a1 X
to utter that the product is not a product in
a1 X
and of course then too we will be left to discuss nothing at all about the X.
Let R be a proper subring of a ring R'. Let x be a member of R' not in
R. A finite expression a_0 + a_1 X + a_2 X^2 +... has members a_0,
a_1,... in R. The whole thing is a member of R'. The sums are sums and
the products are products. This approach to polynomials will be found
in volume I of van der Waerden.
But Peter is it clean? Isn't this essentially unioning X with the reals in the case of polynomials with real coefficients?
It won't work out
I doubt that you've every worked anything out. It's standard first year
stuff to show that if R is a ring then R[X] (however defined) is also a
ring.
Post by Timothy Golden
. It already offends the ring requirements. I simply put before you again the black swan
1.23 X
which is not to evaluate to a single element in your new set
It's very obviously an element of R'.
Post by Timothy Golden
. Please name this element for me.
Penelope? Frederick?
Post by Timothy Golden
I think in your terseness you do see the problem. Possibly van der Waerden avoids the closure requirement in his build
That's an idiotic suggestion.
Post by Timothy Golden
. It sure would be helpful to have an electronic link to the text you are using.
Do you have a title or ISBN or something like that?
The sum is not a sum.
The product not a product.
And the X is nothing at all.
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
Who is on first? Where is second? Elementary dear Watson!
Two is one and one is two!
I hear proclaimed from the AA hall of truth and justice for all.
Now you've really got it Peter! By jove, son, this man is really onto something.
Timothy Golden
2020-11-21 00:18:24 UTC
Post by Timothy Golden
Post by Timothy Golden
Thus it is for you who utters that the sum is not a sum in
a0 + a1 X
to utter that the product is not a product in
a1 X
and of course then too we will be left to discuss nothing at all about the X.
Let R be a proper subring of a ring R'. Let x be a member of R' not in
R. A finite expression a_0 + a_1 X + a_2 X^2 +... has members a_0,
a_1,... in R. The whole thing is a member of R'. The sums are sums and
the products are products. This approach to polynomials will be found
in volume I of van der Waerden.
But Peter is it clean? Isn't this essentially unioning X with the reals in the case of polynomials with real coefficients?
It won't work out
I doubt that you've every worked anything out. It's standard first year
stuff to show that if R is a ring then R[X] (however defined) is also a
ring.
Post by Timothy Golden
. It already offends the ring requirements. I simply put before you again the black swan
1.23 X
which is not to evaluate to a single element in your new set
It's very obviously an element of R'.
Post by Timothy Golden
. Please name this element for me.
Penelope? Frederick?
Post by Timothy Golden
I think in your terseness you do see the problem. Possibly van der Waerden avoids the closure requirement in his build
That's an idiotic suggestion.
Post by Timothy Golden
. It sure would be helpful to have an electronic link to the text you are using.
Do you have a title or ISBN or something like that?
The sum is not a sum.
The product not a product.
And the X is nothing at all.
--
When, once, reference was made to a statesman almost universally
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
-> The sum is not a sum. >-> The product not a product. >-> And the X is nothing at all.
my signature for this thread? At least then you only have to delete one line of it. Oh, if I delete one line of yours then it won't be your sig will it? Done.

Pretty sure Peter we are down to set theory. Elements are nameable entities in a well defined set. If
1.23
is an element of the set and
X
is an element of the set then
1.23 X
are two elements of the set in product, right? There is an operator present right? This is where you are supposed to utter like the chicken that you are: "that product is not the product." Oh, one is two and two is one, eh, Peter? Cluck, cluck.
Peter
2020-11-21 10:41:27 UTC
Post by Timothy Golden
Post by Timothy Golden
Post by Timothy Golden
Thus it is for you who utters that the sum is not a sum in
a0 + a1 X
to utter that the product is not a product in
a1 X
and of course then too we will be left to discuss nothing at all about the X.
Let R be a proper subring of a ring R'. Let x be a member of R' not in
R. A finite expression a_0 + a_1 X + a_2 X^2 +... has members a_0,
a_1,... in R. The whole thing is a member of R'. The sums are sums and
the products are products. This approach to polynomials will be found
in volume I of van der Waerden.
But Peter is it clean? Isn't this essentially unioning X with the reals in the case of polynomials with real coefficients?
It won't work out
I doubt that you've every worked anything out. It's standard first year
stuff to show that if R is a ring then R[X] (however defined) is also a
ring.
Post by Timothy Golden
. It already offends the ring requirements. I simply put before you again the black swan
1.23 X
which is not to evaluate to a single element in your new set
It's very obviously an element of R'.
Post by Timothy Golden
. Please name this element for me.
Penelope? Frederick?
Post by Timothy Golden
I think in your terseness you do see the problem. Possibly van der Waerden avoids the closure requirement in his build
That's an idiotic suggestion.
Post by Timothy Golden
. It sure would be helpful to have an electronic link to the text you are using.
Do you have a title or ISBN or something like that?
The sum is not a sum.
The product not a product.
And the X is nothing at all.
--
When, once, reference was made to a statesman almost universally
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
-> The sum is not a sum. >-> The product not a product. >-> And the X is nothing at all.
my signature for this thread? At least then you only have to delete one line of it. Oh, if I delete one line of yours then it won't be your sig will it? Done.
Pretty sure Peter we are down to set theory. Elements are nameable entities in a well defined set. If
1.23
is an element of the set and
X
is an element of the set then
1.23 X
are two elements of the set in product, right? There is an operator present right? This is where you are supposed to utter like the chicken that you are: "that product is not the product.
I don't say that. 1.23 and X are both members (if you don't like
elements) of a ring, then their product 1.23 X are also members of that
ring.
Post by Timothy Golden
" Oh, one is two and two is one, eh, Peter? Cluck, cluck.
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
Timothy Golden
2020-11-21 17:02:43 UTC
Post by Timothy Golden
Post by Timothy Golden
Post by Timothy Golden
Thus it is for you who utters that the sum is not a sum in
a0 + a1 X
to utter that the product is not a product in
a1 X
and of course then too we will be left to discuss nothing at all about the X.
Let R be a proper subring of a ring R'. Let x be a member of R' not in
R. A finite expression a_0 + a_1 X + a_2 X^2 +... has members a_0,
a_1,... in R. The whole thing is a member of R'. The sums are sums and
the products are products. This approach to polynomials will be found
in volume I of van der Waerden.
But Peter is it clean? Isn't this essentially unioning X with the reals in the case of polynomials with real coefficients?
It won't work out
I doubt that you've every worked anything out. It's standard first year
stuff to show that if R is a ring then R[X] (however defined) is also a
ring.
Post by Timothy Golden
. It already offends the ring requirements. I simply put before you again the black swan
1.23 X
which is not to evaluate to a single element in your new set
It's very obviously an element of R'.
Post by Timothy Golden
. Please name this element for me.
Penelope? Frederick?
Post by Timothy Golden
I think in your terseness you do see the problem. Possibly van der Waerden avoids the closure requirement in his build
That's an idiotic suggestion.
Post by Timothy Golden
. It sure would be helpful to have an electronic link to the text you are using.
Do you have a title or ISBN or something like that?
The sum is not a sum.
The product not a product.
And the X is nothing at all.
--
When, once, reference was made to a statesman almost universally
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
-> The sum is not a sum. >-> The product not a product. >-> And the X is nothing at all.
my signature for this thread? At least then you only have to delete one line of it. Oh, if I delete one line of yours then it won't be your sig will it? Done.
Pretty sure Peter we are down to set theory. Elements are nameable entities in a well defined set. If
1.23
is an element of the set and
X
is an element of the set then
1.23 X
are two elements of the set in product, right? There is an operator present right? This is where you are supposed to utter like the chicken that you are: "that product is not the product.
I don't say that. 1.23 and X are both members (if you don't like
elements) of a ring, then their product 1.23 X are also members of that
ring.
Post by Timothy Golden
" Oh, one is two and two is one, eh, Peter? Cluck, cluck.
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
I have no trouble naming them as elements. The fact remains that the set was never carefully constructed. It is as if for you the usage of the word
ring
engages some sort of super fairy dust that gets all sorts of new devices on your swiss army knife. Tools like these are not practical. They are frivolous. The snapped blade; the one that folds back onto your fingers; the little phillips screwdriver that will get your hand good and tired of driving screws, especially after the thing strips a bit. Now, bringing the analogy down to the math with seriousness Peter, I have to ask whether
1.23 X
is one element or two elements? It seems to me that your answer is yes to both. Really the sham that is AA is here under your nose now Peter. Why has it taken us this long to get here? Whose impedance was it? Certainly it was not mine. I suggested as much months ago; that the conversation must turn to elemental analysis in set theory. Then too we must harken right back to the ring and its careful definition of operators. Do operators yield a single element? Ought they yield two? three? Come now, I'm fairly certain that we all know the answer is one. When I do
1 + 2 = 3
is this the addition operator of the ring? Give it a jingle Peter. I'm sure you have not forgotten how to count, though you may be into a new form if you stand by AA. Two equals one; turtles all the way down. Cheers, Peter, for finally facing the black swan.
-> The sum is not a sum. >-> The product not a product. >-> And the X is nothing at all.
Peter
2020-11-23 23:55:01 UTC
Post by Timothy Golden
Post by Timothy Golden
Post by Timothy Golden
Post by Timothy Golden
Thus it is for you who utters that the sum is not a sum in
a0 + a1 X
to utter that the product is not a product in
a1 X
and of course then too we will be left to discuss nothing at all about the X.
Let R be a proper subring of a ring R'. Let x be a member of R' not in
R. A finite expression a_0 + a_1 X + a_2 X^2 +... has members a_0,
a_1,... in R. The whole thing is a member of R'. The sums are sums and
the products are products. This approach to polynomials will be found
in volume I of van der Waerden.
But Peter is it clean? Isn't this essentially unioning X with the reals in the case of polynomials with real coefficients?
It won't work out
I doubt that you've every worked anything out. It's standard first year
stuff to show that if R is a ring then R[X] (however defined) is also a
ring.
Post by Timothy Golden
. It already offends the ring requirements. I simply put before you again the black swan
1.23 X
which is not to evaluate to a single element in your new set
It's very obviously an element of R'.
Post by Timothy Golden
. Please name this element for me.
Penelope? Frederick?
Post by Timothy Golden
I think in your terseness you do see the problem. Possibly van der Waerden avoids the closure requirement in his build
That's an idiotic suggestion.
Post by Timothy Golden
. It sure would be helpful to have an electronic link to the text you are using.
Do you have a title or ISBN or something like that?
The sum is not a sum.
The product not a product.
And the X is nothing at all.
--
When, once, reference was made to a statesman almost universally
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
-> The sum is not a sum. >-> The product not a product. >-> And the X is nothing at all.
my signature for this thread? At least then you only have to delete one line of it. Oh, if I delete one line of yours then it won't be your sig will it? Done.
Pretty sure Peter we are down to set theory. Elements are nameable entities in a well defined set. If
1.23
is an element of the set and
X
is an element of the set then
1.23 X
are two elements of the set in product, right? There is an operator present right? This is where you are supposed to utter like the chicken that you are: "that product is not the product.
I don't say that. 1.23 and X are both members (if you don't like
elements) of a ring, then their product 1.23 X are also members of that
ring.
Post by Timothy Golden
" Oh, one is two and two is one, eh, Peter? Cluck, cluck.
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
I have no trouble naming them as elements. The fact remains that the set was never carefully constructed. It is as if for you the usage of the word
ring
engages some sort of super fairy dust that gets all sorts of new devices on your swiss army knife. Tools like these are not practical. They are frivolous. The snapped blade; the one that folds back onto your fingers; the little phillips screwdriver that will get your hand good and tired of driving screws, especially after the thing strips a bit. Now, bringing the analogy down to the math with seriousness Peter, I have to ask whether
1.23 X
is one element or two elements? It seems to me that your answer is yes to both. Really the sham that is AA is here under your nose now Peter. Why has it taken us this long to get here? Whose impedance was it? Certainly it was not mine. I suggested as much months ago; that the conversation must turn to elemental analysis in set theory. Then too we must harken right back to the ring and its careful definition of operators. Do operators yield a single element? Ought they yield two? three? Come now, I'm fairly certain that we all know the answer is one. When I do
1 + 2 = 3
is this the addition operator of the ring? Give it a jingle Peter. I'm sure you have not forgotten how to count, though you may be into a new form if you stand by AA. Two equals one; turtles all the way down. Cheers, Peter, for finally facing the black swan.
-> The sum is not a sum. >-> The product not a product. >-> And the X is nothing at all.
I don't know why you're struggling with this. If you don't understand
any of what follows, tell me what you don't understand. Try not to go
off on tangents about black swans, ethics committees and fairy tales.

Let R be the ring of real numbers. There is a ring R' such that R is a
proper subring of R'. Let X be any member of R' that is not a member of
R. Expressions of the form (where the a_i are members of R)

a_0 + a_1 X + a_2 X^2 +...+ a_n X^n

collectively constitute a ring with addition and multiplication defined
in the obvious way.

Ok?
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
FredJeffries
2020-11-18 19:13:45 UTC
1.23 X
where 1.23 is a real value and X is not a real value and so this product offends the closure requirement of the ring definition
I have a REALLY stupid question: Does
1/2 + 1/2 = 1
also offend the closure requirement for addition in the ring of integers and does
sqrt(2)*sqrt(2) = 2
similarly offend the closure requirement for multiplication in the ring of integers?
Timothy Golden
2020-11-19 23:44:37 UTC
Post by FredJeffries
1.23 X
where 1.23 is a real value and X is not a real value and so this product offends the closure requirement of the ring definition
I have a REALLY stupid question: Does
1/2 + 1/2 = 1
also offend the closure requirement for addition in the ring of integers and does
sqrt(2)*sqrt(2) = 2
similarly offend the closure requirement for multiplication in the ring of integers?
That's a neat way to go at it. Seems more like you were working in the ring of rationals and then the ring of reals though. The loose usage of X is very close by in that it is never specified in terms of set theory. One text I have even describes X as a "variable" (quotes theirs without really ever looking back seriously on why) . The subterfuge that I am pointing to I believe is much stronger than the subterfuge that you've created, but yours does help fill out the space a bit I think. By the time we get to the reals there is no more of that subsetting type of behavior going on right? AA makes free usage of the "polynomial with real coefficients". The ring behavior of the outward polynomials is well expressed, but upon dismantling the polynomial down to a single term
1.23 X
we see the utter failure to follow the ring requirements. One earlier correspondent here did want to claim that AA formally unions the X into the reals, but I don't think it was a whole hearted attempt. If it were true then the match to your own argument is pretty clear.
zelos...@gmail.com
2020-11-20 06:07:39 UTC
Post by Timothy Golden
Post by FredJeffries
1.23 X
where 1.23 is a real value and X is not a real value and so this product offends the closure requirement of the ring definition
I have a REALLY stupid question: Does
1/2 + 1/2 = 1
also offend the closure requirement for addition in the ring of integers and does
sqrt(2)*sqrt(2) = 2
similarly offend the closure requirement for multiplication in the ring of integers?
That's a neat way to go at it. Seems more like you were working in the ring of rationals and then the ring of reals though. The loose usage of X is very close by in that it is never specified in terms of set theory. One text I have even describes X as a "variable" (quotes theirs without really ever looking back seriously on why) . The subterfuge that I am pointing to I believe is much stronger than the subterfuge that you've created, but yours does help fill out the space a bit I think. By the time we get to the reals there is no more of that subsetting type of behavior going on right? AA makes free usage of the "polynomial with real coefficients". The ring behavior of the outward polynomials is well expressed, but upon dismantling the polynomial down to a single term
1.23 X
we see the utter failure to follow the ring requirements. One earlier correspondent here did want to claim that AA formally unions the X into the reals, but I don't think it was a whole hearted attempt. If it were true then the match to your own argument is pretty clear.
FredJeffries
2020-11-20 17:15:33 UTC
Post by Timothy Golden
Post by FredJeffries
1.23 X
where 1.23 is a real value and X is not a real value and so this product offends the closure requirement of the ring definition
I have a REALLY stupid question: Does
1/2 + 1/2 = 1
also offend the closure requirement for addition in the ring of integers and does
sqrt(2)*sqrt(2) = 2
similarly offend the closure requirement for multiplication in the ring of integers?
That's a neat way to go at it. Seems more like you were working in the ring of rationals and then the ring of reals though.
I merely ask because you seem to have the usual notion of 'closure' backwards.

Usually, a binary operation * is said to be closed over a set A iff whenever b and c are elements of A, b*c is also an element of A.

But YOU seem to be saying that whenever b*c is an element of A then b and c must also be elements of A
FromTheRafters
2020-11-20 20:18:46 UTC
Post by FredJeffries
Post by Timothy Golden
Post by FredJeffries
Post by Timothy Golden
Again, I find your own stance to be agreeable to mine; it's just that we
are yielding starkly different conclusions. As to who is running a status
quo campaign here and who is the underdog in this fight... your own
misstep legitimates my very concern. In following this train of thought
and returning again to the black swan whose singular operator is known to
be a product: 1.23 X where 1.23 is a real value and X is not a real
value and so this product offends the closure requirement of the ring
definition
I have a REALLY stupid question: Does
1/2 + 1/2 = 1
also offend the closure requirement for addition in the ring of integers
and does sqrt(2)*sqrt(2) = 2
similarly offend the closure requirement for multiplication in the ring of integers?
That's a neat way to go at it. Seems more like you were working in the ring
of rationals and then the ring of reals though.
I merely ask because you seem to have the usual notion of 'closure' backwards.
Usually, a binary operation * is said to be closed over a set A iff whenever
b and c are elements of A, b*c is also an element of A.
But YOU seem to be saying that whenever b*c is an element of A then b and c
must also be elements of A
I think you need to have (some of) the inverse elements. IOW for
addition you need negative numbers and for multiplication you need
rationals or units.
FredJeffries
2020-11-20 21:21:53 UTC
Post by FromTheRafters
Post by FredJeffries
Post by Timothy Golden
Post by FredJeffries
Post by Timothy Golden
Again, I find your own stance to be agreeable to mine; it's just that we
are yielding starkly different conclusions. As to who is running a status
quo campaign here and who is the underdog in this fight... your own
misstep legitimates my very concern. In following this train of thought
and returning again to the black swan whose singular operator is known to
be a product: 1.23 X where 1.23 is a real value and X is not a real
value and so this product offends the closure requirement of the ring
definition
I have a REALLY stupid question: Does
1/2 + 1/2 = 1
also offend the closure requirement for addition in the ring of integers
and does sqrt(2)*sqrt(2) = 2
similarly offend the closure requirement for multiplication in the ring of
integers?
That's a neat way to go at it. Seems more like you were working in the ring
of rationals and then the ring of reals though.
I merely ask because you seem to have the usual notion of 'closure' backwards.
Usually, a binary operation * is said to be closed over a set A iff whenever
b and c are elements of A, b*c is also an element of A.
But YOU seem to be saying that whenever b*c is an element of A then b and c
must also be elements of A
I think you need to have (some of) the inverse elements. IOW for
addition you need negative numbers and for multiplication you need
rationals or units.
Really? You have been involved in this more than I. All I can figure that he is saying is that
1.23X
cannot be in the ring of polynomials because 1.23 is a real number and X has some special meaning in his 'ring'.

(never mind that 1.23 and X are BOTH members of the ring of (real) polynomials).
FromTheRafters
2020-11-20 22:47:53 UTC
Post by FredJeffries
Post by FromTheRafters
Post by FredJeffries
Post by Timothy Golden
Post by FredJeffries
Post by Timothy Golden
Again, I find your own stance to be agreeable to mine; it's just that we
are yielding starkly different conclusions. As to who is running a
status quo campaign here and who is the underdog in this fight... your
own misstep legitimates my very concern. In following this train of
thought and returning again to the black swan whose singular operator
is known to be a product: 1.23 X where 1.23 is a real value and X is
not a real value and so this product offends the closure requirement of
the ring definition
I have a REALLY stupid question: Does
1/2 + 1/2 = 1
also offend the closure requirement for addition in the ring of integers
and does sqrt(2)*sqrt(2) = 2
similarly offend the closure requirement for multiplication in the ring
of integers?
That's a neat way to go at it. Seems more like you were working in the
ring of rationals and then the ring of reals though.
I merely ask because you seem to have the usual notion of 'closure' backwards.
Usually, a binary operation * is said to be closed over a set A iff
whenever b and c are elements of A, b*c is also an element of A.
But YOU seem to be saying that whenever b*c is an element of A then b and c
must also be elements of A
I think you need to have (some of) the inverse elements. IOW for
addition you need negative numbers and for multiplication you need
rationals or units.
Really? You have been involved in this more than I. All I can figure that he
is saying is that 1.23X
cannot be in the ring of polynomials because 1.23 is a real number and X has
some special meaning in his 'ring'.
(never mind that 1.23 and X are BOTH members of the ring of (real) polynomials).
One can add, subtract, and multiply. What is it that is 'offending' or
'not ring behaved' in this scenario?
zelos...@gmail.com
2020-11-19 06:57:52 UTC
Post by Timothy Golden
Fascinating. You really are holding to that singular argument. Again I credit you with persistence
Why wouldn't I hold it when that is where you go wrong?
Post by Timothy Golden
I suppose I am forced at this point to insist upon the exact equivalence between the ordinary polynomial form and the ordered series notation
The SEQUENCE is THE CONSTRUCTION, the NOTATION is what you think polynomials are.
Post by Timothy Golden
Would you care to cite a work which does in fact disabuse the ordinary polynomial format? If you cannot find one which insists that the format is old and endangered as you so readily admit, then where does this leave your own argument?
There is no issue using the old school notation with the understanding that it is notation from old times.
https://proofwiki.org/wiki/Definition:Polynomial_Ring/Monoid_Ring_on_Natural_Numbers
https://proofwiki.org/wiki/Definition:Polynomial_Ring/Sequences
Post by Timothy Golden
Again, I find your own stance to be agreeable to mine; it's just that we are yielding starkly different conclusions. As to who is running a status quo campaign here and who is the underdog in this fight... your own misstep legitimates my very concern.
We don't because I understand the differens between notation and the object, you clearly don't.
Post by Timothy Golden
In following this train of thought and returning again to the black swan whose singular operator is known to be a product
It is nothing of the sort.
Post by Timothy Golden
1.23 X
Is notation for (0,1.23,0,0,...), nothing else, no product.
Post by Timothy Golden
where 1.23 is a real value and X is not a real value
is a colloqial understanding of it because it is more intuitive when you start early in mathematics than the formal construction.

Real numbers are thought of as by normal people as "numbers with infintie decimals" but that is a wrong understanding, but sufficient for them. Formally it is not that cause it is just notation.
Post by Timothy Golden
and so this product offends the closure requirement of the ring definition
It offends nothing and fails nothing because you are arguing based on notation, not the construction.

(0,1.23,0,0,0,...) does not in anyway "offend" anything, it is an element of |R^|N just fine.
Post by Timothy Golden
And yet the subject completely hinges and relies upon the claim that these polynomials are ring behaved.
They are
https://proofwiki.org/wiki/Definition:Ring_of_Sequences_of_Finite_Support

as you can see here, sum, differens and product remain a sequence always. Closure is achieved.
Post by Timothy Golden
Thus it is for you who utters that the sum is not a sum in
You can view those as a sum but you gotta understand then that a_0+a_1X means (a_0,0,0,...)+(0,a_1,0,0,0,...)=(a_0,a_1,0,0,0,...), at which of course it is easier to just understand the sum in those cases as notation anyway.
Post by Timothy Golden
It is already enough for me that you deny the sum
You really have an issue with understanding the differens between notation and the object itself.
Post by Timothy Golden
It is already enough for me that you deny the polynomial form.
I do not deny that it is the notational form, I just say that is all it is. Notation.
Post by Timothy Golden
I gave you above, as I have done before and you clearly did not read.
Post by Timothy Golden
And why would it be that the polynomial form has to go away?
The classical way of writing doesn't have to go away, it is perfectly fine because most people, you clearly excluded, when they start dealing with the idea of rings, has the mental capacity to understand the differens between notation and the object it represents. You fail at this.
Post by Timothy Golden
It can only be for exactly the reasons that I expose to the public here and that get swept under the carpet by you here.
Nope, again, the traditional writing do not need to go, you however need to educate yourself.
Post by Timothy Golden
AA is as fraudulent a topic as you are a debater.
I am not a debater and we are not having a debate. I am an educator and I am educating you where you are wrong.
Post by Timothy Golden
Still in a moment of egalitarianism I must credit you for staying on here, but you must see how weak your own position is.
Given you only attack NOTATION, the weakness is with you. You have never once said "it is not a ring by its construction", which is where it matters.
Post by Timothy Golden
I will try to remain open and accept your seriousness as well. It is possible that the empire can strike back. If it does so in lies that it believes authentically in, and this is the position of all who are mistaken, then so can I do the same. Let us run our truth saber through this material please.
Read what I give you then
Timothy Golden
2020-11-20 15:49:16 UTC
Post by ***@gmail.com
Post by Timothy Golden
Fascinating. You really are holding to that singular argument. Again I credit you with persistence
Why wouldn't I hold it when that is where you go wrong?
Post by Timothy Golden
I suppose I am forced at this point to insist upon the exact equivalence between the ordinary polynomial form and the ordered series notation
The SEQUENCE is THE CONSTRUCTION, the NOTATION is what you think polynomials are.
Post by Timothy Golden
Would you care to cite a work which does in fact disabuse the ordinary polynomial format? If you cannot find one which insists that the format is old and endangered as you so readily admit, then where does this leave your own argument?
There is no issue using the old school notation with the understanding that it is notation from old times.
https://proofwiki.org/wiki/Definition:Polynomial_Ring/Monoid_Ring_on_Natural_Numbers
https://proofwiki.org/wiki/Definition:Polynomial_Ring/Sequences
Well I will not cower away from your links as you do mine Zelos. The Sequences link above here does formalize a function which maps a raw coefficient into the ordered series form. This is not a unidirectional thing sir. We can travel both ways via such a construction. Your inability to face the equivalence between the traditional polynomial and the ordered series form portrays perfectly the topic of AA. Skating on thin ice. The ice literally cracking under foot; all that there is to do is to skate faster. Well, you simply are headed for thinner ice. I recommend the thick stuff. Head for shore before you are sunk.

If you wish to disabuse abstract algebra of the traditional polynomial form then why bother using the terminology? Is it a polynomial you are working in or isn't it? Your own practice of dodging this simple question does nothing for your argument. Please now, this is not a matter of notation. Notation as convention versus breaking the closure requirement as the black swan
1.23 X
does are two very different things. Yes, I do believe that notation matters, and here really you are the one who is sunk for it is your insistence on the ordered notation that your argument hinges upon with no ability to look back. These are two parallel universes with exact correspondence. You have yet to state what exactly makes the ordered form superior for fear that you will be attacking the original polynomial form. This stupidity is yours in the making.

Zelos the whipping boy comes back for more every time. Hang on a minute, the ends are getting frayed again. Let me just singe down the cord so we can get a few good lashes in again. Now bend over Zelos... It's for a good cause, right?
Post by ***@gmail.com
Post by Timothy Golden
Again, I find your own stance to be agreeable to mine; it's just that we are yielding starkly different conclusions. As to who is running a status quo campaign here and who is the underdog in this fight... your own misstep legitimates my very concern.
We don't because I understand the differens between notation and the object, you clearly don't.
Post by Timothy Golden
In following this train of thought and returning again to the black swan whose singular operator is known to be a product
It is nothing of the sort.
Post by Timothy Golden
1.23 X
Is notation for (0,1.23,0,0,...), nothing else, no product.
Post by Timothy Golden
where 1.23 is a real value and X is not a real value
is a colloqial understanding of it because it is more intuitive when you start early in mathematics than the formal construction.
Real numbers are thought of as by normal people as "numbers with infintie decimals" but that is a wrong understanding, but sufficient for them. Formally it is not that cause it is just notation.
Post by Timothy Golden
and so this product offends the closure requirement of the ring definition
It offends nothing and fails nothing because you are arguing based on notation, not the construction.
(0,1.23,0,0,0,...) does not in anyway "offend" anything, it is an element of |R^|N just fine.
Post by Timothy Golden
And yet the subject completely hinges and relies upon the claim that these polynomials are ring behaved.
They are
https://proofwiki.org/wiki/Definition:Ring_of_Sequences_of_Finite_Support
as you can see here, sum, differens and product remain a sequence always. Closure is achieved.
Post by Timothy Golden
Thus it is for you who utters that the sum is not a sum in
You can view those as a sum but you gotta understand then that a_0+a_1X means (a_0,0,0,...)+(0,a_1,0,0,0,...)=(a_0,a_1,0,0,0,...), at which of course it is easier to just understand the sum in those cases as notation anyway.
Post by Timothy Golden
It is already enough for me that you deny the sum
You really have an issue with understanding the differens between notation and the object itself.
Post by Timothy Golden
It is already enough for me that you deny the polynomial form.
I do not deny that it is the notational form, I just say that is all it is. Notation.
Post by Timothy Golden
I gave you above, as I have done before and you clearly did not read.
Post by Timothy Golden
And why would it be that the polynomial form has to go away?
The classical way of writing doesn't have to go away, it is perfectly fine because most people, you clearly excluded, when they start dealing with the idea of rings, has the mental capacity to understand the differens between notation and the object it represents. You fail at this.
Post by Timothy Golden
It can only be for exactly the reasons that I expose to the public here and that get swept under the carpet by you here.
Nope, again, the traditional writing do not need to go, you however need to educate yourself.
Post by Timothy Golden
AA is as fraudulent a topic as you are a debater.
I am not a debater and we are not having a debate. I am an educator and I am educating you where you are wrong.
Post by Timothy Golden
Still in a moment of egalitarianism I must credit you for staying on here, but you must see how weak your own position is.
Given you only attack NOTATION, the weakness is with you. You have never once said "it is not a ring by its construction", which is where it matters.
Post by Timothy Golden
I will try to remain open and accept your seriousness as well. It is possible that the empire can strike back. If it does so in lies that it believes authentically in, and this is the position of all who are mistaken, then so can I do the same. Let us run our truth saber through this material please.
Read what I give you then
zelos...@gmail.com
2020-11-23 07:00:33 UTC
Post by Timothy Golden
Well I will not cower away from your links as you do mine Zelos
I don't cower yours, the issue is you focus only on notation.
Post by Timothy Golden
The Sequences link above here does formalize a function which maps a raw coefficient into the ordered series form
Which is the formal construction of polynomials.
Post by Timothy Golden
Your inability to face the equivalence between the traditional polynomial and the ordered series form portrays perfectly the topic of AA
The issue here is that you conflate traditional polynomial NOTATION! with the actual object which is what I have said ALL ALONG.
Post by Timothy Golden
If you wish to disabuse abstract algebra of the traditional polynomial form then why bother using the terminology?
Why call it polynomials? History, thats why. It is called imaginary numbers due to history, not because they do not exist.
Post by Timothy Golden
Is it a polynomial you are working in or isn't it?
We call the objects in the ring R[x] for polynomials, their formal construction is done through sequences and we write it as sums.
Post by Timothy Golden
Your own practice of dodging this simple question does nothing for your argument
I have dodged none of your questions.
Post by Timothy Golden
Please now, this is not a matter of notation.
It is.
Post by Timothy Golden
Notation as convention versus breaking the closure requirement
There is no berakign of the closure requirement, the issue is that you do not understand that the complaint you try to raise is just notation.
Post by Timothy Golden
1.23 X
is notation for (0,1.23,0,0,0,...), it has no product in it so it is NOT a fucking violation of closure.
Post by Timothy Golden
Zelos the whipping boy comes back for more every time
Whipping boy? HAH! Comes from the one failing mathematics here adn cannot seperate notation from a construction issue! You are pathetic in your arrogance.
Timothy Golden
2020-11-23 13:49:55 UTC
Post by ***@gmail.com
1.23 X
is notation for (0,1.23,0,0,0,...), it has no product in it so it is NOT a fucking violation of closure.
There we have it!
The product is no product!
The sum is not a sum.
And X is nothing at all.

Thank you again and again Zelos. You are at least a third of the way there. Now lets shift over to the sum in
a0 + a1 X
where this is a polynomial with real coefficients. Are you willing to bark that this sum is not a sum? Please speak out loudly and clearly here. I've got a box of matches ready.
zelos...@gmail.com
2020-11-24 06:20:17 UTC
Post by Timothy Golden
The product is no product!
Except there is no product, so "the product" doesn't refer to anything.
Post by Timothy Golden
Thank you again and again Zelos. You are at least a third of the way there. Now lets shift over to the sum in
You still don't fucking understand the differens between notation and the object itself.

Why do you keep going on about these thigns when I have explained to you it is just notation?
Timothy Golden
2020-11-24 16:21:42 UTC
Post by ***@gmail.com
Post by Timothy Golden
The product is no product!
Except there is no product, so "the product" doesn't refer to anything.
Post by Timothy Golden
Thank you again and again Zelos. You are at least a third of the way there. Now lets shift over to the sum in
You still don't fucking understand the differens between notation and the object itself.
Why do you keep going on about these thigns when I have explained to you it is just notation?
OK, so to do a very minimal interpretation of your own words I think it is fair to say from the Zelos AA view:
Z1: The polynomial with real coefficients does not contain any sums or products.
It won't be much of a stretch to posit that
Z2: The polynomial of abstract algebra in general does not contain any sums or products.

This is very direct reasoning and I am so happy that you have come along this far. I will assume that you do agree with the above two statements and of course if you'd like to make some qualifying remarks then that would be fine. I guess if I could just sharpen up the points on the top and bottom of the X we could have you for lunch over a nice fire. What is that pesky X all about anyways? Your notation has no need of it right? Is it nothing at all? If so then I'll get a pot of soup going first. Hmmm.... bread or rolls? I think rolls.
Peter
2020-11-24 20:18:03 UTC
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
The product is no product!
Except there is no product, so "the product" doesn't refer to anything.
Post by Timothy Golden
Thank you again and again Zelos. You are at least a third of the way there. Now lets shift over to the sum in
You still don't fucking understand the differens between notation and the object itself.
Why do you keep going on about these thigns when I have explained to you it is just notation?
Z1: The polynomial with real coefficients does not contain any sums or products.
It won't be much of a stretch to posit that
Z2: The polynomial of abstract algebra in general does not contain any sums or products.
This is very direct reasoning and I am so happy that you have come along this far. I will assume that you do agree with the above two statements and of course if you'd like to make some qualifying remarks then that would be fine. I guess if I could just sharpen up the points on the top and bottom of the X we could have you for lunch over a nice fire. What is that pesky X all about anyways?
It's a place holder.
Post by Timothy Golden
Your notation has no need of it right? Is it nothing at all? If so then I'll get a pot of soup going first. Hmmm.... bread or rolls? I think rolls.
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
zelos...@gmail.com
2020-11-25 06:36:02 UTC
Post by Timothy Golden
Z1: The polynomial with real coefficients does not contain any sums or products.
(a_0,a_1,a_2,a_3,....)

You tell me, is there a sum or product in the sequence which is THE construction of polynomials?
Post by Timothy Golden
What is that pesky X all about anyways?
Notation that stems from before we formalized polynomials.
Post by Timothy Golden
Your notation has no need of it right?
Maybe it does, maybe it doesn't, it is there however for historical reasons.
Timothy Golden
2020-11-25 13:22:14 UTC
Post by ***@gmail.com
Post by Timothy Golden
Z1: The polynomial with real coefficients does not contain any sums or products.
(a_0,a_1,a_2,a_3,....)
You tell me, is there a sum or product in the sequence which is THE construction of polynomials?
Post by Timothy Golden
What is that pesky X all about anyways?
Notation that stems from before we formalized polynomials.
Post by Timothy Golden
Your notation has no need of it right?
Maybe it does, maybe it doesn't, it is there however for historical reasons.
It is where Zelos? The X that is that might or might not be needed in your opinion.
I don't see it anywhere in your work. so far on this thread. In fact you haven't shown us much here.
You've done plenty for my cause already:

The sum is not a sum
The product not a product
And the X might be nothing at all.
zelos...@gmail.com
2020-11-25 13:32:27 UTC
Post by Timothy Golden
It is where Zelos? The X that is that might or might not be needed in your opinion.
It is just notation, it is influenced by history and convinience.
Not really, the issue is still, you are stuck on notation.

POolynomials are constructed using sequences (a_0,a_1,a_2,a_3,...)

Answer me now, where is the sum here?
Where is the product?
Where is the X?
Timothy Golden
2020-11-26 15:33:56 UTC
Post by ***@gmail.com
Post by Timothy Golden
It is where Zelos? The X that is that might or might not be needed in your opinion.
It is just notation, it is influenced by history and convinience.
Not really, the issue is still, you are stuck on notation.
POolynomials are constructed using sequences (a_0,a_1,a_2,a_3,...)
Answer me now, where is the sum here?
Where is the product?
Where is the X?
The problem seems to land us in elemental analysis.
Which is more fundamental:
1. ( a0, 0, 0, 0, 0, ... )
2. a0
3. none of the above
4. all of the above
5. AA is for shit-heals and this question will never be answered by such brainwashed morons.

Your comfort with requiring an infinity of terms is deeply troubling.

That your comfort grows when you explain that only a finite number of them are nonzero is a relief for some, but not for me.

For me simplicity will always rule mathematics and if I were to propose to you that in a two valued system that one value was not more fundamental than two values, well, I would hope that you would call me out on this detail, especially if my entire theory rests on this sharp point.

Let's harken back to something familiar like (x,y) coordinates. We know that we will be able to as well develop (x,y,z) coordinates, but as to what these individual values are... this lands us discussing x coordinates first. That which is fundamental is elemental. It may be true that one day molecular structures will be worked with in their advanced state without the need to drop down to their elemental basis in atoms, but as they are dismantled and dissected if we fail to land in an atomic basis then the new concept of refactoring will take on some rather interesting twists and turns. Yes, this is possible, but it would then imply a rewriting of the elemental form; a new atomic theory.

We cannot claim the elements to be molecular. This is a simplistic structural error, and yet as I complain about the mathematicians and their lack of compiler level integrity I see that the branch of AA has taken this mis-step. There are other similar errors. You are not alone. AA cowards need cower alone no more. The Cartesian product is abused thoroughly as far as I can tell, and oddly enough there it is just above. And again there it is buried in the ring definition down so low that you won't bother to go there until I shove your nose in it. Your masters own shit, rub your face around in it while you gasp for air, fill your mouth with it, hold it in and lick it onto to the sharpened tops of the X. I pity any who fall onto the thing. It was not of my making. I am taking it down.
Timothy Golden
2020-11-26 17:31:04 UTC
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
It is where Zelos? The X that is that might or might not be needed in your opinion.
It is just notation, it is influenced by history and convinience.
Not really, the issue is still, you are stuck on notation.
POolynomials are constructed using sequences (a_0,a_1,a_2,a_3,...)
Answer me now, where is the sum here?
Where is the product?
Where is the X?
The problem seems to land us in elemental analysis.
1. ( a0, 0, 0, 0, 0, ... )
2. a0
3. none of the above
4. all of the above
5. AA is for shit-heals and this question will never be answered by such brainwashed morons.
Your comfort with requiring an infinity of terms is deeply troubling.
That your comfort grows when you explain that only a finite number of them are nonzero is a relief for some, but not for me.
For me simplicity will always rule mathematics and if I were to propose to you that in a two valued system that one value was not more fundamental than two values, well, I would hope that you would call me out on this detail, especially if my entire theory rests on this sharp point.
Let's harken back to something familiar like (x,y) coordinates. We know that we will be able to as well develop (x,y,z) coordinates, but as to what these individual values are... this lands us discussing x coordinates first. That which is fundamental is elemental. It may be true that one day molecular structures will be worked with in their advanced state without the need to drop down to their elemental basis in atoms, but as they are dismantled and dissected if we fail to land in an atomic basis then the new concept of refactoring will take on some rather interesting twists and turns. Yes, this is possible, but it would then imply a rewriting of the elemental form; a new atomic theory.
We cannot claim the elements to be molecular. This is a simplistic structural error, and yet as I complain about the mathematicians and their lack of compiler level integrity I see that the branch of AA has taken this mis-step. There are other similar errors. You are not alone. AA cowards need cower alone no more. The Cartesian product is abused thoroughly as far as I can tell, and oddly enough there it is just above. And again there it is buried in the ring definition down so low that you won't bother to go there until I shove your nose in it. Your masters own shit, rub your face around in it while you gasp for air, fill your mouth with it, hold it in and lick it onto to the sharpened tops of the X. I pity any who fall onto the thing. It was not of my making. I am taking it down.
p.s. Happy Thankstaking to all Americans North and South... may the indigenous peoples have their day in court and let them feast as we have feasted on their lands. I'm on my second cup of coffee today. Cheers, Power, and Justice, for All. May the proxy system be exposed everywhere it operates.
zelos...@gmail.com
2020-11-27 06:17:53 UTC
For what?
Post by Timothy Golden
Your comfort with requiring an infinity of terms is deeply troubling.
Its a sequence, not a term. And why is it troubling that it is a sequence of infinite length?
Post by Timothy Golden
That your comfort grows when you explain that only a finite number of them are nonzero is a relief for some, but not for me.
What comfort are you even on about? I hold no discomfort or comfort with them because it is simply the way it is constructed in order to cover all cases.
Post by Timothy Golden
For me simplicity will always rule mathematics
1: Who cares what is for you? You don't dictate mathematics
2: It is the simplest way to cover all cases in a formal manner.
Post by Timothy Golden
if I were to propose to you that in a two valued system that one value was not more fundamental than two values, well, I would hope that you would call me out on this detail, especially if my entire theory rests on this sharp point
What are you on about here?
Post by Timothy Golden
this lands us discussing x coordinates first. That which is fundamental is elemental.
Discussing to understand something conceptually is not the same as formalyl constructing something.
Post by Timothy Golden
It may be true that one day molecular structures
And who cares? This is mathematics, not physics.
Post by Timothy Golden
This is a simplistic structural error, and yet as I complain about the mathematicians and their lack of compiler level integrity I see that the branch of AA has taken this mis-step.
You have yet to show any "misstep" that isn't you conflating notation with the object.

The objects we call polynomials are formally defined as sequences where almost all values are zero.

Where is the sum?
Where is the product?
Where is the X you complain about?

Where in (a_0,a_1,a_2,a_3,...) is any of those 3?

If you complain about those, you need to point out where in that it is because that is the formal construction.

The finite sum/product of sequences of almost all zero values equals a sequence of almost all zero values. So it is 100% entirely closed and sates the closure axiom.
Post by Timothy Golden
The Cartesian product is abused thoroughly as far as I can tell, and oddly enough there it is just above
Care to point out where it has been abused? Becuase sequences are not cartesian products.
Post by Timothy Golden
And again there it is buried in the ring definition down so low that you won't bother to go there until I shove your nose in it
Where? Go ahead and show, as stated, The finite sum/product of sequences of almost all zero values equals a sequence of almost all zero values. So it is 100% entirely closed and sates the closure axiom.

So that is not violated in construction of polynomials. So again, where is the issue?

You must use the formal constructions to raise objections, otherwise you are wrong from the get go.
Timothy Golden
2020-11-27 17:25:48 UTC
Post by ***@gmail.com
For what?
Post by Timothy Golden
Your comfort with requiring an infinity of terms is deeply troubling.
Its a sequence, not a term. And why is it troubling that it is a sequence of infinite length?
Post by Timothy Golden
That your comfort grows when you explain that only a finite number of them are nonzero is a relief for some, but not for me.
What comfort are you even on about? I hold no discomfort or comfort with them because it is simply the way it is constructed in order to cover all cases.
Post by Timothy Golden
For me simplicity will always rule mathematics
1: Who cares what is for you? You don't dictate mathematics
2: It is the simplest way to cover all cases in a formal manner.
Post by Timothy Golden
if I were to propose to you that in a two valued system that one value was not more fundamental than two values, well, I would hope that you would call me out on this detail, especially if my entire theory rests on this sharp point
What are you on about here?
Post by Timothy Golden
this lands us discussing x coordinates first. That which is fundamental is elemental.
Discussing to understand something conceptually is not the same as formalyl constructing something.
Post by Timothy Golden
It may be true that one day molecular structures
And who cares? This is mathematics, not physics.
Post by Timothy Golden
This is a simplistic structural error, and yet as I complain about the mathematicians and their lack of compiler level integrity I see that the branch of AA has taken this mis-step.
You have yet to show any "misstep" that isn't you conflating notation with the object.
The objects we call polynomials are formally defined as sequences where almost all values are zero.
Where is the sum?
Where is the product?
Where is the X you complain about?
Where in (a_0,a_1,a_2,a_3,...) is any of those 3?
I love it. Thank you Zelos. You have completed the mantra. You are a true AA devotee; the type that will gladly fall on the X.

Now bend over once again Zelos. I have the frays singed. Middle of the X. Don't you worry about those shit stains.
Post by ***@gmail.com
If you complain about those, you need to point out where in that it is because that is the formal construction.
The finite sum/product of sequences of almost all zero values equals a sequence of almost all zero values. So it is 100% entirely closed and sates the closure axiom.
Post by Timothy Golden
The Cartesian product is abused thoroughly as far as I can tell, and oddly enough there it is just above
Care to point out where it has been abused? Becuase sequences are not cartesian products.
Post by Timothy Golden
And again there it is buried in the ring definition down so low that you won't bother to go there until I shove your nose in it
Where? Go ahead and show, as stated, The finite sum/product of sequences of almost all zero values equals a sequence of almost all zero values. So it is 100% entirely closed and sates the closure axiom.
So that is not violated in construction of polynomials. So again, where is the issue?
You must use the formal constructions to raise objections, otherwise you are wrong from the get go.
Indeed I do, and you insist on a new form that divorces the work away from the polynomial, so how come you to still even use this word? Does it not map back to the polynomial of old? You seem to believe that something does in fact break when we go back to the original form and yet you refuse to discuss it. Repeatedly. I'm sorry Z, but for any onlooker here I am looking at least matched to you and your methods. I personally see my own position as stronger by a factor of ten, but I am willing to concede that ego is inescapable. What sort of statement did you have on MIT's reference text? This one starting at page 264:
where his excellent writing states:
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."

All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.

The sum is not a sum
The product no product
And X is no thing at all
zelos...@gmail.com
2020-11-30 06:42:23 UTC
Post by Timothy Golden
I love it. Thank you Zelos. You have completed the mantra. You are a true AA devotee; the type that will gladly fall on the X.
Notice how you do not answer the question.
Post by Timothy Golden
Your consideration is so badly spent though that I can't help but believe that I am speaking to someone in the midst of a tantrum.
What tantrum? Are you getting delusional?
Post by Timothy Golden
Notice how you still with all that irrelevant garbage did not answer my question. Where is any of those 3 in the formal construction?
Post by Timothy Golden
Indeed I do
Yet you never do.
Post by Timothy Golden
and you insist on a new form that divorces the work away from the polynomial
I don't. I understand the historical parts of thigns and the actual formal construction. You do not.
Post by Timothy Golden
so how come you to still even use this word?
Why call it integers when we construct them using |Nx|N? Because history gave it that name and we choose to retain it after we formally constructed integers.
Post by Timothy Golden
You seem to believe that something does in fact break when we go back to the original form
No I do not you imbecile, what I do is I point out your question/challange is moot, void, not even wrong, from the get go because you are complaining on notation, not construction.
Post by Timothy Golden
yet you refuse to discuss it
I will discuss with you the formal construction and the formal one alone if you want to say polynomials doesn't work as a ring.

If you want to discuss notation I will discuss notation with you and pros and cons of it and the facts pertaining to it.

I will not however discuss with you "errors" you conjure up based on notation and think it somehow invalidates the construction because that is a massive non-sequitor.
Post by Timothy Golden
I personally see my own position as stronger by a factor of ten
That is called the dunning-krüger effect.
Post by Timothy Golden
but I am willing to concede that ego is inescapable
Maybe you can learn some humilitary and learn proper things then?
Post by Timothy Golden
All the while he does not seem terribly concerned about format the way you are.
Simple, mathematicians have no issue going on the former because we understand the differens between notation and construction, unlike you.

You cannot complain about things related to notation when you try to address construction.
Post by Timothy Golden
Meanwhile you specify no reason that the two constructions belie different concepts.
The one you go for is not a different construction, it is just notation. IF someone tried to use what you say as construction then yes, we have a lot of issues and I can point it out but that is NOT the construction, that is just NOTATION today. What I give IS THE formal construction.
Post by Timothy Golden
The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.
1: It is a sequence
2: It is rigorous and how it is properly done.
3: Again, yours is not a construction (it never could be ofrmally) it is notation and you can easily go between both, but you are too stupid to do it hence we gotta be strict.
Timothy Golden
2020-12-02 11:50:10 UTC
Post by ***@gmail.com
Post by Timothy Golden
I love it. Thank you Zelos. You have completed the mantra. You are a true AA devotee; the type that will gladly fall on the X.
Notice how you do not answer the question.
Post by Timothy Golden
Your consideration is so badly spent though that I can't help but believe that I am speaking to someone in the midst of a tantrum.
What tantrum? Are you getting delusional?
Post by Timothy Golden
Notice how you still with all that irrelevant garbage did not answer my question. Where is any of those 3 in the formal construction?
Post by Timothy Golden
Indeed I do
Yet you never do.
Post by Timothy Golden
and you insist on a new form that divorces the work away from the polynomial
I don't. I understand the historical parts of thigns and the actual formal construction. You do not.
Post by Timothy Golden
so how come you to still even use this word?
Why call it integers when we construct them using |Nx|N? Because history gave it that name and we choose to retain it after we formally constructed integers.
Post by Timothy Golden
You seem to believe that something does in fact break when we go back to the original form
No I do not you imbecile, what I do is I point out your question/challange is moot, void, not even wrong, from the get go because you are complaining on notation, not construction.
Post by Timothy Golden
yet you refuse to discuss it
I will discuss with you the formal construction and the formal one alone if you want to say polynomials doesn't work as a ring.
If you want to discuss notation I will discuss notation with you and pros and cons of it and the facts pertaining to it.
I will not however discuss with you "errors" you conjure up based on notation and think it somehow invalidates the construction because that is a massive non-sequitor.
Post by Timothy Golden
I personally see my own position as stronger by a factor of ten
That is called the dunning-krüger effect.
Post by Timothy Golden
but I am willing to concede that ego is inescapable
Maybe you can learn some humilitary and learn proper things then?
Post by Timothy Golden
All the while he does not seem terribly concerned about format the way you are.
Simple, mathematicians have no issue going on the former because we understand the differens between notation and construction, unlike you.
You seem to believe that something does in fact break when we go back to the original form and yet you refuse to discuss it. Repeatedly. I'm sorry Z, but for any onlooker here I am looking at least matched to you and your methods. I personally see my own position as stronger by a factor of ten, but I am willing to concede that ego is inescapable. What sort of statement did you have on MIT's reference text? This one starting at page 264:
where his excellent writing states:
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."

All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.

The sum is not a sum
The product no product
And X is no thing at all
Post by ***@gmail.com
You cannot complain about things related to notation when you try to address construction.
Post by Timothy Golden
Meanwhile you specify no reason that the two constructions belie different concepts.
The one you go for is not a different construction, it is just notation. IF someone tried to use what you say as construction then yes, we have a lot of issues and I can point it out but that is NOT the construction, that is just NOTATION today. What I give IS THE formal construction.
Post by Timothy Golden
The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.
1: It is a sequence
2: It is rigorous and how it is properly done.
3: Again, yours is not a construction (it never could be ofrmally) it is notation and you can easily go between both, but you are too stupid to do it hence we gotta be strict.
zelos...@gmail.com
2020-12-03 06:21:48 UTC
Post by Timothy Golden
You seem to believe that something does in fact break when we go back to the original form
No I don't because again, IT IS JUST NOTATION!
Post by Timothy Golden
yet you refuse to discuss it
IT IS NOTATION! How hard is that to understand?
Post by Timothy Golden
I'm sorry Z, but for any onlooker here I am looking at least matched to you and your methods.
Not anyone that knows mathematics.

Now, do you wish to discuss notation, or do you wish to discuss construction?

Pick one or the other, not both

If you wanna talk about "sum/product", then its notation at which you cannot claim "it is broken"

If you wanna discuss construction and claim it is broken, then we do the formal construction as I have given.
Timothy Golden
2020-12-05 17:28:34 UTC
Post by ***@gmail.com
Post by Timothy Golden
You seem to believe that something does in fact break when we go back to the original form
No I don't because again, IT IS JUST NOTATION!
Post by Timothy Golden
yet you refuse to discuss it
IT IS NOTATION! How hard is that to understand?
Post by Timothy Golden
I'm sorry Z, but for any onlooker here I am looking at least matched to you and your methods.
Not anyone that knows mathematics.
Now, do you wish to discuss notation, or do you wish to discuss construction?
Pick one or the other, not both
If you wanna talk about "sum/product", then its notation at which you cannot claim "it is broken"
If you wanna discuss construction and claim it is broken, then we do the formal construction as I have given.
You seem to believe that something does in fact break when we go back to the original form and yet you refuse to discuss it. Repeatedly. I'm sorry Z, but for any onlooker here I am looking at least matched to you and your methods. I personally see my own position as stronger by a factor of ten, but I am willing to concede that ego is inescapable. What sort of statement did you have on MIT's reference text? This one starting at page 264:
where his excellent writing states:
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."

All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.

The sum is not a sum
The product no product
And X is no thing at all
zelos...@gmail.com
2020-12-07 07:14:32 UTC
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
You seem to believe that something does in fact break when we go back to the original form
No I don't because again, IT IS JUST NOTATION!
Post by Timothy Golden
yet you refuse to discuss it
IT IS NOTATION! How hard is that to understand?
Post by Timothy Golden
I'm sorry Z, but for any onlooker here I am looking at least matched to you and your methods.
Not anyone that knows mathematics.
Now, do you wish to discuss notation, or do you wish to discuss construction?
Pick one or the other, not both
If you wanna talk about "sum/product", then its notation at which you cannot claim "it is broken"
If you wanna discuss construction and claim it is broken, then we do the formal construction as I have given.
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."
All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.
The sum is not a sum
The product no product
And X is no thing at all
So I take it you have nothign to come with?
Timothy Golden
2020-12-07 15:56:18 UTC
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
You seem to believe that something does in fact break when we go back to the original form
No I don't because again, IT IS JUST NOTATION!
Post by Timothy Golden
yet you refuse to discuss it
IT IS NOTATION! How hard is that to understand?
Post by Timothy Golden
I'm sorry Z, but for any onlooker here I am looking at least matched to you and your methods.
Not anyone that knows mathematics.
Now, do you wish to discuss notation, or do you wish to discuss construction?
Pick one or the other, not both
If you wanna talk about "sum/product", then its notation at which you cannot claim "it is broken"
If you wanna discuss construction and claim it is broken, then we do the formal construction as I have given.
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."
All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.
The sum is not a sum
The product no product
And X is no thing at all
So I take it you have nothign to come with?
You seem to believe that something does in fact break when we go back to the original form and yet you refuse to discuss it. Repeatedly. I'm sorry Z, but for any onlooker here I am looking at least matched to you and your methods. I personally see my own position as stronger by a factor of ten, but I am willing to concede that ego is inescapable. What sort of statement did you have on MIT's reference text? This one starting at page 264:
where his excellent writing states:
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."

All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.

The sum is not a sum
The product no product
And X is no thing at all
zelos...@gmail.com
2020-12-08 06:33:15 UTC
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
You seem to believe that something does in fact break when we go back to the original form
No I don't because again, IT IS JUST NOTATION!
Post by Timothy Golden
yet you refuse to discuss it
IT IS NOTATION! How hard is that to understand?
Post by Timothy Golden
I'm sorry Z, but for any onlooker here I am looking at least matched to you and your methods.
Not anyone that knows mathematics.
Now, do you wish to discuss notation, or do you wish to discuss construction?
Pick one or the other, not both
If you wanna talk about "sum/product", then its notation at which you cannot claim "it is broken"
If you wanna discuss construction and claim it is broken, then we do the formal construction as I have given.
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."
All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.
The sum is not a sum
The product no product
And X is no thing at all
So I take it you have nothign to come with?
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."
All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.
The sum is not a sum
The product no product
And X is no thing at all
so here we have it, you going full on bassam crank when you cannot come with anything genuine.
Timothy Golden
2020-12-09 20:12:40 UTC
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
You seem to believe that something does in fact break when we go back to the original form
No I don't because again, IT IS JUST NOTATION!
Post by Timothy Golden
yet you refuse to discuss it
IT IS NOTATION! How hard is that to understand?
Post by Timothy Golden
I'm sorry Z, but for any onlooker here I am looking at least matched to you and your methods.
Not anyone that knows mathematics.
Now, do you wish to discuss notation, or do you wish to discuss construction?
Pick one or the other, not both
If you wanna talk about "sum/product", then its notation at which you cannot claim "it is broken"
If you wanna discuss construction and claim it is broken, then we do the formal construction as I have given.
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."
All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.
The sum is not a sum
The product no product
And X is no thing at all
So I take it you have nothign to come with?
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."
All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.
The sum is not a sum
The product no product
And X is no thing at all
so here we have it, you going full on bassam crank when you cannot come with anything genuine.
I'm sorry; my bot seems to have broken down. I do apologize. I happen to like some of King Bassam's criticism, but he's never engaged in authentic communication with me. An orb such as I rarely meets one who can keep up. Your own bottiness really is relentless here. I have no choice but to return in kind.
zelos...@gmail.com
2020-12-10 06:31:43 UTC
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
You seem to believe that something does in fact break when we go back to the original form
No I don't because again, IT IS JUST NOTATION!
Post by Timothy Golden
yet you refuse to discuss it
IT IS NOTATION! How hard is that to understand?
Post by Timothy Golden
I'm sorry Z, but for any onlooker here I am looking at least matched to you and your methods.
Not anyone that knows mathematics.
Now, do you wish to discuss notation, or do you wish to discuss construction?
Pick one or the other, not both
If you wanna talk about "sum/product", then its notation at which you cannot claim "it is broken"
If you wanna discuss construction and claim it is broken, then we do the formal construction as I have given.
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."
All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.
The sum is not a sum
The product no product
And X is no thing at all
So I take it you have nothign to come with?
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."
All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.
The sum is not a sum
The product no product
And X is no thing at all
so here we have it, you going full on bassam crank when you cannot come with anything genuine.
I'm sorry; my bot seems to have broken down. I do apologize. I happen to like some of King Bassam's criticism, but he's never engaged in authentic communication with me. An orb such as I rarely meets one who can keep up. Your own bottiness really is relentless here. I have no choice but to return in kind.
Bassam has offered no genuine critique because like you, he refuses to address things at the proper point. Like you, he is a crank.

I am ready to discuss things properly with you, or anyone here.

So I ask again, do you wish to discuss the notation, where a_0+a_1X+a_2 X^2+.... resides

or do you wish to discuss the properties, and thereby construction, of |R[X], which involves the set {x e |R^|N: |{y e |N: x(y)~=0}|<aleph_0}?
Timothy Golden
2020-12-11 00:02:27 UTC
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
You seem to believe that something does in fact break when we go back to the original form
No I don't because again, IT IS JUST NOTATION!
Post by Timothy Golden
yet you refuse to discuss it
IT IS NOTATION! How hard is that to understand?
Post by Timothy Golden
I'm sorry Z, but for any onlooker here I am looking at least matched to you and your methods.
Not anyone that knows mathematics.
Now, do you wish to discuss notation, or do you wish to discuss construction?
Pick one or the other, not both
If you wanna talk about "sum/product", then its notation at which you cannot claim "it is broken"
If you wanna discuss construction and claim it is broken, then we do the formal construction as I have given.
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."
All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.
The sum is not a sum
The product no product
And X is no thing at all
So I take it you have nothign to come with?
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."
All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.
The sum is not a sum
The product no product
And X is no thing at all
so here we have it, you going full on bassam crank when you cannot come with anything genuine.
I'm sorry; my bot seems to have broken down. I do apologize. I happen to like some of King Bassam's criticism, but he's never engaged in authentic communication with me. An orb such as I rarely meets one who can keep up. Your own bottiness really is relentless here. I have no choice but to return in kind.
Bassam has offered no genuine critique because like you, he refuses to address things at the proper point. Like you, he is a crank.
I am ready to discuss things properly with you, or anyone here.
So I ask again, do you wish to discuss the notation, where a_0+a_1X+a_2 X^2+.... resides
or do you wish to discuss the properties, and thereby construction, of |R[X], which involves the set {x e |R^|N: |{y e |N: x(y)~=0}|<aleph_0}?
OK Z. I'll have them put that on your sarcophogus.
zelos...@gmail.com
2020-12-11 06:25:27 UTC
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
You seem to believe that something does in fact break when we go back to the original form
No I don't because again, IT IS JUST NOTATION!
Post by Timothy Golden
yet you refuse to discuss it
IT IS NOTATION! How hard is that to understand?
Post by Timothy Golden
I'm sorry Z, but for any onlooker here I am looking at least matched to you and your methods.
Not anyone that knows mathematics.
Now, do you wish to discuss notation, or do you wish to discuss construction?
Pick one or the other, not both
If you wanna talk about "sum/product", then its notation at which you cannot claim "it is broken"
If you wanna discuss construction and claim it is broken, then we do the formal construction as I have given.
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."
All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.
The sum is not a sum
The product no product
And X is no thing at all
So I take it you have nothign to come with?
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."
All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.
The sum is not a sum
The product no product
And X is no thing at all
so here we have it, you going full on bassam crank when you cannot come with anything genuine.
I'm sorry; my bot seems to have broken down. I do apologize. I happen to like some of King Bassam's criticism, but he's never engaged in authentic communication with me. An orb such as I rarely meets one who can keep up. Your own bottiness really is relentless here. I have no choice but to return in kind.
Bassam has offered no genuine critique because like you, he refuses to address things at the proper point. Like you, he is a crank.
I am ready to discuss things properly with you, or anyone here.
So I ask again, do you wish to discuss the notation, where a_0+a_1X+a_2 X^2+.... resides
or do you wish to discuss the properties, and thereby construction, of |R[X], which involves the set {x e |R^|N: |{y e |N: x(y)~=0}|<aleph_0}?
OK Z. I'll have them put that on your sarcophogus.
Which is it you wish to discuss, notation or peroperties/construction?

Why is it when I try to have a genuine discussion with yuo and tie it down properly, you won't even bother?
Timothy Golden
2020-12-11 12:24:09 UTC
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
You seem to believe that something does in fact break when we go back to the original form
No I don't because again, IT IS JUST NOTATION!
Post by Timothy Golden
yet you refuse to discuss it
IT IS NOTATION! How hard is that to understand?
Post by Timothy Golden
I'm sorry Z, but for any onlooker here I am looking at least matched to you and your methods.
Not anyone that knows mathematics.
Now, do you wish to discuss notation, or do you wish to discuss construction?
Pick one or the other, not both
If you wanna talk about "sum/product", then its notation at which you cannot claim "it is broken"
If you wanna discuss construction and claim it is broken, then we do the formal construction as I have given.
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."
All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.
The sum is not a sum
The product no product
And X is no thing at all
So I take it you have nothign to come with?
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."
All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.
The sum is not a sum
The product no product
And X is no thing at all
so here we have it, you going full on bassam crank when you cannot come with anything genuine.
I'm sorry; my bot seems to have broken down. I do apologize. I happen to like some of King Bassam's criticism, but he's never engaged in authentic communication with me. An orb such as I rarely meets one who can keep up. Your own bottiness really is relentless here. I have no choice but to return in kind.
Bassam has offered no genuine critique because like you, he refuses to address things at the proper point. Like you, he is a crank.
I am ready to discuss things properly with you, or anyone here.
So I ask again, do you wish to discuss the notation, where a_0+a_1X+a_2 X^2+.... resides
or do you wish to discuss the properties, and thereby construction, of |R[X], which involves the set {x e |R^|N: |{y e |N: x(y)~=0}|<aleph_0}?
OK Z. I'll have them put that on your sarcophogus.
Which is it you wish to discuss, notation or peroperties/construction?
Why is it when I try to have a genuine discussion with yuo and tie it down properly, you won't even bother?
Zelos you have assumed the position of garbage collector on this thread really from the beginning. Now it is at the end and it is time to say good-bye. Good-bye to a fraud curriculum. Good-bye to dancing professors who wave their hand over here to cover up what they just wrote over there. To morons who insist on an infinite series of components to develop the complex plane from real numbers. Good-bye Abstract Algebra (AA). Goodbye to your abusive ways; The ring was lost long ago and just one creature knows its whereabouts now. Why does this topic seem so preccccioousss to you? In the dark your eyes have grown so large that when dragged out kicking and screaming in the full power of the great fusion reactor in the sky your blood curdling screams only raise confusion from ordinary passers by. I cannot cleanly call this escapism that you practice in this department. It is much closer to masochism.
zelos...@gmail.com
2020-12-14 07:58:21 UTC
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
You seem to believe that something does in fact break when we go back to the original form
No I don't because again, IT IS JUST NOTATION!
Post by Timothy Golden
yet you refuse to discuss it
IT IS NOTATION! How hard is that to understand?
Post by Timothy Golden
I'm sorry Z, but for any onlooker here I am looking at least matched to you and your methods.
Not anyone that knows mathematics.
Now, do you wish to discuss notation, or do you wish to discuss construction?
Pick one or the other, not both
If you wanna talk about "sum/product", then its notation at which you cannot claim "it is broken"
If you wanna discuss construction and claim it is broken, then we do the formal construction as I have given.
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."
All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.
The sum is not a sum
The product no product
And X is no thing at all
So I take it you have nothign to come with?
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."
All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.
The sum is not a sum
The product no product
And X is no thing at all
so here we have it, you going full on bassam crank when you cannot come with anything genuine.
I'm sorry; my bot seems to have broken down. I do apologize. I happen to like some of King Bassam's criticism, but he's never engaged in authentic communication with me. An orb such as I rarely meets one who can keep up. Your own bottiness really is relentless here. I have no choice but to return in kind.
Bassam has offered no genuine critique because like you, he refuses to address things at the proper point. Like you, he is a crank.
I am ready to discuss things properly with you, or anyone here.
So I ask again, do you wish to discuss the notation, where a_0+a_1X+a_2 X^2+.... resides
or do you wish to discuss the properties, and thereby construction, of |R[X], which involves the set {x e |R^|N: |{y e |N: x(y)~=0}|<aleph_0}?
OK Z. I'll have them put that on your sarcophogus.
Which is it you wish to discuss, notation or peroperties/construction?
Why is it when I try to have a genuine discussion with yuo and tie it down properly, you won't even bother?
Zelos you have assumed the position of garbage collector on this thread really from the beginning. Now it is at the end and it is time to say good-bye. Good-bye to a fraud curriculum. Good-bye to dancing professors who wave their hand over here to cover up what they just wrote over there. To morons who insist on an infinite series of components to develop the complex plane from real numbers. Good-bye Abstract Algebra (AA). Goodbye to your abusive ways; The ring was lost long ago and just one creature knows its whereabouts now. Why does this topic seem so preccccioousss to you? In the dark your eyes have grown so large that when dragged out kicking and screaming in the full power of the great fusion reactor in the sky your blood curdling screams only raise confusion from ordinary passers by. I cannot cleanly call this escapism that you practice in this department. It is much closer to masochism.
Why should we say good bye to things that work, just because you are too stupid to understand
Timothy Golden
2020-12-16 20:13:47 UTC
Post by ***@gmail.com
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
Post by ***@gmail.com
Post by Timothy Golden
You seem to believe that something does in fact break when we go back to the original form
No I don't because again, IT IS JUST NOTATION!
Post by Timothy Golden
yet you refuse to discuss it
IT IS NOTATION! How hard is that to understand?
Post by Timothy Golden
I'm sorry Z, but for any onlooker here I am looking at least matched to you and your methods.
Not anyone that knows mathematics.
Now, do you wish to discuss notation, or do you wish to discuss construction?
Pick one or the other, not both
If you wanna talk about "sum/product", then its notation at which you cannot claim "it is broken"
If you wanna discuss construction and claim it is broken, then we do the formal construction as I have given.
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."
All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.
The sum is not a sum
The product no product
And X is no thing at all
So I take it you have nothign to come with?
"It is probably no surprise that polynomials form a ring. In this chapter we
shall emphasize the algebraic structure of polynomials by studying polynomial
rings. We can prove many results for polynomial rings that are similar to
the theorems we proved for the integers. Analogs of prime numbers, of the
division algorithm, and of the Euclidean algorithm exist for polynomials."
All the while he does not seem terribly concerned about format the way you are. Meanwhile you specify no reason that the two constructions belie different concepts. The ordered series is simply more cryptic. What inhibits the travel back and forth between the two as identical? You seem to have no idea, and yet your insistence is unconditional.
The sum is not a sum
The product no product
And X is no thing at all
so here we have it, you going full on bassam crank when you cannot come with anything genuine.
I'm sorry; my bot seems to have broken down. I do apologize. I happen to like some of King Bassam's criticism, but he's never engaged in authentic communication with me. An orb such as I rarely meets one who can keep up. Your own bottiness really is relentless here. I have no choice but to return in kind.
Bassam has offered no genuine critique because like you, he refuses to address things at the proper point. Like you, he is a crank.
I am ready to discuss things properly with you, or anyone here.
So I ask again, do you wish to discuss the notation, where a_0+a_1X+a_2 X^2+.... resides
or do you wish to discuss the properties, and thereby construction, of |R[X], which involves the set {x e |R^|N: |{y e |N: x(y)~=0}|<aleph_0}?
OK Z. I'll have them put that on your sarcophogus.
Which is it you wish to discuss, notation or peroperties/construction?
Why is it when I try to have a genuine discussion with yuo and tie it down properly, you won't even bother?
Zelos you have assumed the position of garbage collector on this thread really from the beginning. Now it is at the end and it is time to say good-bye. Good-bye to a fraud curriculum. Good-bye to dancing professors who wave their hand over here to cover up what they just wrote over there. To morons who insist on an infinite series of components to develop the complex plane from real numbers. Good-bye Abstract Algebra (AA). Goodbye to your abusive ways; The ring was lost long ago and just one creature knows its whereabouts now. Why does this topic seem so preccccioousss to you? In the dark your eyes have grown so large that when dragged out kicking and screaming in the full power of the great fusion reactor in the sky your blood curdling screams only raise confusion from ordinary passers by. I cannot cleanly call this escapism that you practice in this department. It is much closer to masochism.
Why should we say good bye to things that work, just because you are too stupid to understand
The binary operator definition is crap. When addition is not Abelian it is not addition. There is no need of any Cartesian product. Elements in a set. That is all that is needed. AA is a flop.
a
a + b
a + b + c
a + b + c + d
These are all addition; addition is not a binary operator. It is an n-ary operator. The singleton is included in this. Your own polynomial is included in this, yet, in your attachment you now claim that addition is not present in the polynomial. What a lame stance you've been driven into. I can tell you how you got there.
zelos...@gmail.com
2020-12-17 06:19:30 UTC
Post by Timothy Golden
The binary operator definition is crap
Why? Because you don't understand it?
Post by Timothy Golden
It is common to use the addition symbol when it is abelian, but not a requirement.
Post by Timothy Golden
There is no need of any Cartesian product.
To define a binary operator you need to use cartesian products to make it meaningful in the language of mathematics.
Post by Timothy Golden
AA is a flop
By your previous statement, it is clear your understanding is a flop. You understand that a function is from ONE SET to ANOTHER SET, it means taking ONE ELEMENT from ONE SET and map it to ONE ELEMENT in ONE SET

So to make a binary operator, we need to make a cartesian product which is a method to create ONE SET from TWO OR MORE SETS.

This is not abstract algebra, this is basic fucking mathematics.
Post by Timothy Golden
These are all addition; addition is not a binary operator. It is an n-ary operator.
Correct, which means we must have a cartesian product because a function officially only takes 1 set
Post by Timothy Golden
The singleton is included in this. Your own polynomial is included in this, yet, in your attachment you now claim that addition is not present in the polynomial. What a lame stance you've been driven into. I can tell you how you got there.
You keep not understanding the differens between notation, that may include a lot of things not present, for historical reasons or sake of convinience.
dy/dx does not mean a quotient, it means derivation for example, but it is historically written so.
Timothy Golden
2020-12-22 18:30:39 UTC
Post by ***@gmail.com
Post by Timothy Golden
The binary operator definition is crap
Why? Because you don't understand it?
Post by Timothy Golden
It is common to use the addition symbol when it is abelian, but not a requirement.
Post by Timothy Golden
There is no need of any Cartesian product.
dy/dx does not mean a quotient, it means derivation for example, but it is historically written so.
I'm sorry but this bit here is crap actually. The line formula
y = m x + b
is for instance such a slope.
( y - b ) / x = m = y / x - b / x

I believe the zero intercept being present in this form becomes trivial but think of it as hauling the origin to any point along the line and we'll have a nice bit of relativity built in. All along the line the slope is
delta y / delta x
and you can pick widely and inadvertently; as carelessly as the AA'ers have done. Cheers!
zelos...@gmail.com
2021-01-04 06:13:58 UTC
Post by Timothy Golden
I'm sorry but this bit here is crap actually.
Just because you don't understand it?
Post by Timothy Golden
The line formula
Is not the derivative
Post by Timothy Golden
I believe the zero intercept being present in this form becomes trivial but think of it as hauling the origin to any point along the line and we'll have a nice bit of relativity built in. All along the line the slope is
Correct, that is FOR A LINE, but NOT FOR ALL DERIVATIVES WHICH ARE NOT LINES.
zelos...@gmail.com
2020-10-26 09:41:20 UTC
Post by Tim Golden BandTech.com
Post by Lalo T.
Maybe there are much more better symbol compared with the symbol '&'.
< I may have discovered polysign but I'm prepared to pass the torch here
Giving up something in what you have put a big amount of energy that easy ?
No I'll never give up, but you deserve huge recognition. The energy you are spending on exhaustive background research I could never manage. And so far I don't think I'd ever discover this reciprocal either. Hopefully I'll get to a point where I can wrap my head around it, but Like Newton's gravitational theory: it only gets to be discovered once Lalo.
I did post a guess at the P4 reciprocal, but google is now truncating text so you have to click on the blue text at the bottom of posts here at the moment.
Still haven't gotten up the gumption on proving it but it should be quite doable using the text editor as I did for P3. A lot more cancellations... I have sage running here but I'm nowhere near to knowing how to enter these into it...
sage: 5^5
3125
sage: 4^4
256
sage: 5!
File "<ipython-input-6-8de0a076b17c>", line 1
Integer(5)!
^
SyntaxError: invalid syntax
sage: help(factorial)
sage: factorial(5)
120
sage: 120/5
24
sage: 0.5^3
0.125000000000000
sage: 4^4
256
Post by Lalo T.
< It is a wonderful opening into number theory isn't it?
well, it could be added that the product rule does not have to be necessarily tied
to "cyclic stuff", or latin squares, but, undoubtedly, it is more attractive.
https://en.wikipedia.org/wiki/Latin_square
I see the 'orthogonal representation' has some similarity, but I don't really see distribution in the puzzle. I'm thinking there is an argument out of pure symmetry that will do.
Post by Lalo T.
< which do not map here on my computer.
https://en.wikipedia.org/wiki/Miscellaneous_Technical#/media/File:U+23E7.svg
< I am still tempted to put the # component in another place
( &1 / z₁ ) = ( &1·G·H·K / z₁·G·H·K )
well, you could put an arbitrary G, H, K etc
It is like root rationalisation, but "sign rationalization"
Suppose that in the denominator you have something, and
*1/(something)
...multiplying
(*1·H) / (something·H)
...you get
when a > b
< ( * a * b * c ) (P3)
mmm, now that you mention, it is not essential multiplying by ( * a * b * c ) !!
But, if you don use it the denominator would have more terms, although the max
degree of the terms will be n-1
Seems to work very nicely with it. In terms of dealing in concrete values it clearly does not do much, but in terms of the proof it is enforcing symmetry. It's got to be there to get your cubic terms in P3. It is the most peculiar of the bunch. Very excellent. Fascinating. Subtle. Neutral. Really it has to be there to develop the cancellations too doesn't it? It's like it fills out the thing. It's bringing symmetry to the quantities without upsetting the sign mechanics.
Post by Lalo T.
p4 is not a prime number, hence, a bit more "bad-tempered". The product rule
is "mod 4"...
< ...cancelling bunch so for instance the abccd components
Yes for P5, and further though there are 24 groups of them. Makes me chuckle.
Really this whole thing is very open and maybe there is a grand short cut. I'm enjoying the cryptic dismantling of the thing here. Take your time as you like.
ANswer my question, why won't you argue about the formal construction that I have given you`?
Lalo T.
2020-10-27 00:15:11 UTC
" The distinguished point is just simply one particular point, picked out from
the space, and given a name, such as x0, that remains unchanged during
subsequent discussion, and is kept track of during all operations. "
https://en.wikipedia.org/wiki/Pointed_space
https://en.wikipedia.org/wiki/Origin_(mathematics)
https://en.wikipedia.org/wiki/Pointed_set
(outside of the length components )

in "Even and Odd numbers" section
https://www.allmathtricks.com/number-system-mathematics/#6_Natural_Numbers

https://en.wikipedia.org/wiki/Magma_%28algebra%29#Free_magma

From the concrete to the abstract or viceversa.

I guess that if one invent something new, one has to decide between reuse an
old word, or invent some new one, with the benefit and disadvantages of each one

It would be interesting the geometric justification of the modulus and the
reciprocal of polysigned numbers p4, although tetrahedrons and octahedrons
can be tricky.

Also you could check if the pentachoron is regular in 4d
(in the case of the ring direct sum of two Cs isomorphic to p5 polisigned
numbers ), and finding the "embedded axes" in cartesian and polar coordinates
in order to find the zero-divisors
(even and odd dim.. may differ their behaviour sometimes, one have to check)

At least at coefficient level, one could check if Roger Beresford had a similar
approach, he may not be able to use cancellation in his system, but he can group
together terms :

"I have just checked the division of {a,b,c,d,e} by {e,f,g,h,i} in the
C5 algebra. The answer takes up several pages. Again using a random set of
integers, {3,2,4,8,5}/{2,1,3,2,4} = {269,113,-247,-37,353}/246}. The fifth
roots of unity are five mutually orthogonal unit directions in this system."

https://groupprops.subwiki.org/wiki/Loop
https://en.wikipedia.org/wiki/Quasigroup#Examples
Loops seems to have their own niche...
https://en.wikipedia.org/wiki/List_of_problems_in_loop_theory_and_quasigroup_theory
Lalo T.
2020-10-27 17:23:27 UTC
https://en.wikipedia.org/wiki/Halo_effect
https://en.wikipedia.org/wiki/List_of_animals_with_fraudulent_diplomas
https://en.wikipedia.org/wiki/Postmodernism_Generator
https://en.wikipedia.org/wiki/Wizard_of_Oz_experiment

I guess online encyclopedias are already trying to immunizing against
masive networks of (deliberate) fake sources...

After some time of thought, I think that 'Golden Integers' and 'Golden Rationals'
are well-suited names for integers and rationals in the polysign p5 numbers.

https://en.wikipedia.org/wiki/Icosian

somebody conjectured in the past that zerodivisora in p5 are in the
incommensurable sector.

< When there is a tsunami coming you really ought to run the other way.

an economic one will come to knock my door next month, and I still not have
completed my buoyancy aids, going into...

Peter
2020-10-21 14:42:08 UTC
Tim Golden BandTech.com wrote:
[...]
For the moment it is the ring definition that is under scrutiny, but it is the closure requirement of the ring definition which takes the abuse in the polynomial form as instanced by the polynomial with real coefficient
1.23 X
since 1.23 and X do not belong to the same set
Yes, they do. 1.23 is 1.23,0,0,0,... X is 0,1,0,0,... They are both
members of the set of sequences (of real numbers) that have only
finitely many non-zero elements.

(But at least I now know what your problem is.)
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
Peter
2020-10-21 15:53:37 UTC
[...]
For the moment it is the ring definition that is under scrutiny, but
it is the closure requirement of the ring definition which takes the
abuse in the polynomial form as instanced by the polynomial with real
coefficient
1.23 X
since 1.23 and X do not belong to the same set
Yes, they do.  1.23 is 1.23,0,0,0,...  X is 0,1,0,0,...  They are both
members of the set of sequences (of real numbers) that have only
finitely many non-zero elements.
(But at least I now know what your problem is.)
There is another way of looking at polynomials that says they both
belong to the same set. The coefficients (1.23 for example) belong to a
ring, call it R. Every ring has a more-inclusive ring. Let R' be any
ring such that R is a proper subring of it. Let X be any element of R'
that is not in R, then 1.23 X is a product in R'.
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays
Peter
2020-11-23 18:50:53 UTC
A subring of a ring (R, +, ∗, 0, 1) is a subset S
of R that is both a subgroup of (R, +, 0) and a
submonoid of (R, ∗, 1).
White Swan: S is subgroup and submonoid
Yellow Swan: S is subgroup but not submonoid
I think you mean "Golden swan". But then again, gold and black can be
the same... (https://en.wikipedia.org/wiki/The_dress)
Blue Swan: S is not subgroup but submonoid
Black Swan: S is neither subgroup nor submonoid
This is all a dodge. The instantiated black swan is
1.23 X
which is not ring behaved but as an instance of a polynomial with real
coefficients which is claimed to be ring behaved. This
You need to say what you mean by "ring behaved".  Does it mean anything
other than "in an element of R[X]"?
Oh dear me, "*is* an element of R[X]".
conflict is direct. It is not broad. It is not general. It is extremely
specific.  Just one of these will do in the name of falsification and
the more you dodge it the more you step in it.
< Hmmm? What? Oh, sorry, I didn't see that line that says "1.23 X" and
all the text you repetitively write around it.
< Now you claim to have dismantled the polynomial.
< Hmmm. I must be dreaming. Nope. Back to the usual...
I mean, really, it is as if these high faluting people cannot read.
Can't deal with the simplest of terms.
Dodge what I have put under their noses for the umpteenth time.
I work with a hammer and a chisel while you all pull out your swiss
army knives...
I suppose even your best blade on that thing is dull. And good luck
sharpening it.
And you paid how much for that thing?
--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays