Discussion:
Isn't infinity (in mathematics) actually a flawed concept?
bassam king karzeddin
2017-04-15 12:35:42 UTC
Raw Message
Actually this only concept in mathematics needs few minutes to verify its legality of being considered as any real good and useful concept or just a mere big fallacy that is more than meaningless and a kind of madness, wonder!

It is also stranger how it led the mathematicians to built on it so many huge volumes of baseless mathematics that is good enough for little carpentry works

And even much stranger that they had generated so many types of more infinities to the science of mathematics.

But the oddest thing is that mainstream common mathematicians never realize that such concepts are so meaningless the same way their results that they obtain relying on that fake concept

And naturally such concept is indeed a real paradise for any jugglers to create so many meaningless games and shamelessly consider it as a real science

But the fact that any theorem or formula or result that is associated with such silly concept as infinity, is also so silly but may be good for entertainment

Since mainly, no definite rules with it, nor any real existence (being unreal: by its own definition)

So, this flowed concept would make it very easy in the near future to make mathematics get doubled and tripled and even grows indefinitely in the fake unreal direction to its collapsed limits, for sure

However, many refutations of such meaningless concept was provided in my posts, beside many others

Regards
Bassam King Karzeddin
15 th, April, 2017
b***@gmail.com
2017-04-15 15:25:06 UTC
Raw Message
So sqrt(2) = 1.41421356237... + e, where e is an infinitessimal e <> 0,
and where we have e^2 = 0, i.e. it is nilsquare.

An Invitation to Smooth Infinitesimal Analysis John L. Bell
http://publish.uwo.ca/~jbell/invitation%20to%20SIA.pdf

Or what property does your difference between sqrt(2) and 1.41421356237...
have? There must be a difference when sqrt(2) <> 1.41421356237...

e = sqrt(2) - 1.41421356237...

e <> 0

What property does your infinitessimal e have? Is it nilsquare?
Or does it have some other property?
Post by bassam king karzeddin
Actually this only concept in mathematics needs few minutes to verify its legality of being considered as any real good and useful concept or just a mere big fallacy that is more than meaningless and a kind of madness, wonder!
It is also stranger how it led the mathematicians to built on it so many huge volumes of baseless mathematics that is good enough for little carpentry works
And even much stranger that they had generated so many types of more infinities to the science of mathematics.
But the oddest thing is that mainstream common mathematicians never realize that such concepts are so meaningless the same way their results that they obtain relying on that fake concept
And naturally such concept is indeed a real paradise for any jugglers to create so many meaningless games and shamelessly consider it as a real science
But the fact that any theorem or formula or result that is associated with such silly concept as infinity, is also so silly but may be good for entertainment
Since mainly, no definite rules with it, nor any real existence (being unreal: by its own definition)
So, this flowed concept would make it very easy in the near future to make mathematics get doubled and tripled and even grows indefinitely in the fake unreal direction to its collapsed limits, for sure
However, many refutations of such meaningless concept was provided in my posts, beside many others
Regards
Bassam King Karzeddin
15 th, April, 2017
WM
2017-04-15 15:53:36 UTC
Raw Message
Post by b***@gmail.com
So sqrt(2) = 1.41421356237... + e,
e depends on how many digits you use. But it can only be estimated, not calculated, because sqrt(2) has no decimal representation.

Example: In sqrt(2) = 1.4, e > 0.01421356237.

Regards, WM
b***@gmail.com
2017-04-15 15:56:15 UTC
Raw Message
Well D = 1.41421356237... is a limes its the same as your arithmo-
geometric who knows what figure:

1
1 2
1 2 3
1 2 3 4
...

D is the limes of all chop chops D_n, i.e. D_1 = 1.4, D_2 =1.41, ..
etc.. I didnt ask for sqrt(2) <> D_n, everybody knows that

sqrt(2) <> D_n, because sqrt(2) is irrational.
Post by WM
Post by b***@gmail.com
So sqrt(2) = 1.41421356237... + e,
e depends on how many digits you use. But it can only be estimated, not calculated, because sqrt(2) has no decimal representation.
Example: In sqrt(2) = 1.4, e > 0.01421356237.
Regards, WM
b***@gmail.com
2017-04-15 15:58:51 UTC
Raw Message
So whats the difference between D = lim_n->oo D_n where
D_n = floor(sqrt(2)*10^n)/10^n and sqrt(2):

e = sqrt(2) - D

e <> 0

Is this the case for the reals or not. And if it is the case,
what is this e exactly? Do we have e^2 = 0?
Post by b***@gmail.com
Well D = 1.41421356237... is a limes its the same as your arithmo-
1
1 2
1 2 3
1 2 3 4
...
D is the limes of all chop chops D_n, i.e. D_1 = 1.4, D_2 =1.41, ..
etc.. I didnt ask for sqrt(2) <> D_n, everybody knows that
sqrt(2) <> D_n, because sqrt(2) is irrational.
Post by WM
Post by b***@gmail.com
So sqrt(2) = 1.41421356237... + e,
e depends on how many digits you use. But it can only be estimated, not calculated, because sqrt(2) has no decimal representation.
Example: In sqrt(2) = 1.4, e > 0.01421356237.
Regards, WM
WM
2017-04-15 16:17:29 UTC
Raw Message
Post by b***@gmail.com
So whats the difference between D = lim_n->oo D_n
The limit does exist, but it is not realized or reached by a digit sequence.

where
Post by b***@gmail.com
e = sqrt(2) - D
e <> 0
e = 0. Whether you call the limit sqrt(2) or D does not change anything. The limit is a landmark, not expressible by digits, that remains untouched.
Post by b***@gmail.com
Is this the case for the reals or not. And if it is the case,
what is this e exactly? Do we have e^2 = 0?
e^2 = 0 ==> e = 0.

Regards, WM
b***@gmail.com
2017-04-15 16:20:23 UTC
Raw Message
Post by WM
Whether you call the limit sqrt(2) or D does not change anything.
Can you rigorously proof, that D = sqrt(2), i.e. e = 0?
b***@gmail.com
2017-04-15 16:28:00 UTC
Raw Message
sqrt(2) is not given as a decimal representation here, you
could also imagine that you have rational numbers Q,

and the polynoms Q[X], and then you reduce them via X^2-2=0.
For example to compute:

(1 + sqrt(2))^3

You compute:

(1 + X)^3 = 1 + 3*X + 3*X^2 + X^3

And now you reduce via X^2-2=0 respectively X^2=2, and you get:

= 1 + 3*X + 3*2 + 2*X

= 7 + 5*X

Now you can write sqrt(2) for X again:

= 7 + 5*sqrt(2)

Rational numbers Q, polynoms Q[X] (as syntactic objects) and
the reduction is all pretty finite, no infinity involve.

So a countable language is enought. Check back the result:

7 + 5 sqrt(2)
https://www.wolframalpha.com/input/?i=%281%2Bsqrt%282%29%29^3
Post by b***@gmail.com
Post by WM
Whether you call the limit sqrt(2) or D does not change anything.
Can you rigorously proof, that D = sqrt(2), i.e. e = 0?
WM
2017-04-15 16:35:35 UTC
Raw Message
Post by b***@gmail.com
sqrt(2) is not given as a decimal representation here,
neither is D. D is a limit like sqrt(2). Since D is the limit of the decimal series approximating sqrt(2), D = sqrt(2).

And yes, no infinity is involved. x^2 = D^2 = 2 is enough.

For the first n terms of the decimal sequence we find: they are less than D. But if we choose any real number smaller than D, then we can find a finite term of the decimal sequence which surpasses this smaller number.

Regards, WM

Regards, WM
b***@gmail.com
2017-04-15 20:08:27 UTC
Raw Message
Well D is the decimal representation, 1.41421356237... is just a
shorthand for D = lim n->oo D_n. And its an infinite sequence.

D and sqrt(2) are not "constructed" the same way. sqrt(2) is first
there, and then from sqrt(2) I have defined D_n = floor(sqrt(2)*10^n)/10^n,

and then from D_n I have defined D = lim n->oo D_n. So there was
a process involved going from sqrt(2) to D. And this proces was a

sqrt(2) --> (D_n) --> D

super task, and now we have D = sqrt(2), right? Yes or No?
Post by WM
neither is D. D is a limit like sqrt(2). Since D is the limit of the decimal series approximating sqrt(2), D = sqrt(2).
WM
2017-04-16 18:06:12 UTC
Raw Message
Post by b***@gmail.com
Well D is the decimal representation
No.
Post by b***@gmail.com
, 1.41421356237... is just a
shorthand for D = lim n->oo D_n. And its an infinite sequence.
No. No sequence can define a number because every digit provably fails. You believe that infinity does change this fact?
Post by b***@gmail.com
D and sqrt(2) are not "constructed" the same way.
But both can be approximated step by step.
Post by b***@gmail.com
sqrt(2) is first
there, and then from sqrt(2) I have defined D_n = floor(sqrt(2)*10^n)/10^n,
and then from D_n I have defined D = lim n->oo D_n. So there was
a process involved going from sqrt(2) to D. And this proces was a
sqrt(2) --> (D_n) --> D
super task, and now we have D = sqrt(2), right? Yes or No?
Yes. But D is not expressible by digits.

Regards, WM
w***@gmail.com
2017-04-16 11:53:37 UTC
Raw Message
Post by WM
Post by b***@gmail.com
So whats the difference between D = lim_n->oo D_n
The limit does exist, but it is not realized or reached by a digit sequence.
Of course it depends on what you mean by a "digit sequence"

take sqrt(2) = 1.414...

i: The "standard" interpretation is that the digit sequences is an actual infinite set. (in this case constructable, but that is not needed). It is assumed that all digits are fixed. In this case the limit is determined by
the sequence.

2. WM denies the existence of actual infinite sets. He views the infinite sequence as a potentially infinite set, represented by a finite function, f, on the potentially infinite set of integers. In this case the limit is not determined by the digit sequence, but both the limit and the digit sequence are determined by f. WM is fond of saying that the digit sequence does not define the limit but as any sequence must be associated with an f, which does define the limit, this seems rather pedantic
--
William Hughes
WM
2017-04-16 17:56:27 UTC
Raw Message
Post by w***@gmail.com
Post by WM
Post by b***@gmail.com
So whats the difference between D = lim_n->oo D_n
The limit does exist, but it is not realized or reached by a digit sequence.
Of course it depends on what you mean by a "digit sequence"
take sqrt(2) = 1.414...
i: The "standard" interpretation is that the digit sequences is an actual infinite set. (in this case constructable, but that is not needed). It is assumed that all digits are fixed. In this case the limit is determined by
the sequence.
That is counterfactual belief. For every digit we can prove that it does not determine a number because every digit is at a finite position while infinitely many follow. How can you suppress that fact?
Post by w***@gmail.com
2. WM denies the existence of actual infinite sets. He views the infinite sequence as a potentially infinite set, represented by a finite function, f, on the potentially infinite set of integers. In this case the limit is not determined by the digit sequence, but both the limit and the digit sequence are determined by f.
Yes, you have understood it. Is there a counter *argument*?
Post by w***@gmail.com
WM is fond of saying that the digit sequence does not define the limit but as any sequence must be associated with an f, which does define the limit, this seems rather pedantic
No. There are said to be uncountable many sequences, but there are not uncountably many f.

Regards, WM
pirx42
2017-04-16 18:07:21 UTC
Raw Message
Post by WM
Post by w***@gmail.com
Post by WM
Post by b***@gmail.com
So whats the difference between D = lim_n->oo D_n
The limit does exist, but it is not realized or reached by a digit sequence.
Of course it depends on what you mean by a "digit sequence"
take sqrt(2) = 1.414...
i: The "standard" interpretation is that the digit sequences is an actual infinite set. (in this case constructable, but that is not needed). It is assumed that all digits are fixed. In this case the limit is determined by
the sequence.
That is counterfactual belief. For every digit we can prove that it does not determine a number because every digit is at a finite position while infinitely many follow. How can you suppress that fact?
Post by w***@gmail.com
2. WM denies the existence of actual infinite sets. He views the infinite sequence as a potentially infinite set, represented by a finite function, f, on the potentially infinite set of integers. In this case the limit is not determined by the digit sequence, but both the limit and the digit sequence are determined by f.
Yes, you have understood it. Is there a counter *argument*?
Post by w***@gmail.com
WM is fond of saying that the digit sequence does not define the limit but as any sequence must be associated with an f, which does define the limit, this seems rather pedantic
No. There are said to be uncountable many sequences, but there are not uncountably many f.
Regards, WM
ach
w***@gmail.com
2017-04-16 18:48:51 UTC
Raw Message
On Sunday, April 16, 2017 at 2:56:40 PM UTC-3, WM wrote:

<snip>
Post by WM
No. There are said to be uncountable many sequences, but there are not uncountably many f.
Actually, there are uncountably many f's. Recall, that in the model you use it
may not be true that since every f corresponds to a finite string there is a bijection from the integers to the f's.
--
William Hughes
WM
2017-04-17 18:14:21 UTC
Raw Message
Post by w***@gmail.com
<snip>
Post by WM
No. There are said to be uncountable many sequences, but there are not uncountably many f.
Actually, there are uncountably many f's.
No. In all usable languages there are countably many words including f's.
Post by w***@gmail.com
Recall, that in the model you use it
may not be true that since every f corresponds to a finite string there is a bijection from the integers to the f's.
There is no bijection with all naturals because there are not all naturals. But if there were all naturals, then the f's would not be more.

Regards, WM
w***@gmail.com
2017-04-17 20:21:05 UTC
Raw Message
Post by WM
Post by w***@gmail.com
<snip>
Post by WM
No. There are said to be uncountable many sequences, but there are not uncountably many f.
Actually, there are uncountably many f's.
No. In all usable languages there are countably many words including f's.
Recall, any *subset* of words must be countable. However, it may not be true
that a subcollection of words must be a subset (E.g. If every subset of integers, equivalently every potentially infinite 0/1 sequence, must be computable then the indexes of the halting Turning machines form a subcollection but not a subset). The f's are s subcollection but not a subset.
--
William Hughes
WM
2017-04-18 17:25:47 UTC
Raw Message
Post by w***@gmail.com
Recall, any *subset* of words must be countable. However, it may not be true
that a subcollection of words must be a subset (E.g. If every subset of integers, equivalently every potentially infinite 0/1 sequence, must be computable then the indexes of the halting Turning machines form a subcollection but not a subset). The f's are s subcollection but not a subset.
If you have a countable set S, then every subcollection T is countable and is a set. This is provable by the Axiom of separation. The required predicate is definable with real numbers as parameters in ZFC.

Regards, WM
w***@gmail.com
2017-04-18 19:52:12 UTC
Raw Message
Post by WM
Post by w***@gmail.com
Recall, any *subset* of words must be countable. However, it may not be true
that a subcollection of words must be a subset (E.g. If every subset of integers, equivalently every potentially infinite 0/1 sequence, must be computable then the indexes of the halting Turning machines form a subcollection but not a subset). The f's are s subcollection but not a subset.
If you have a countable set S, then every subcollection T is countable and is a set. This is provable by the Axiom of separation. The required predicate is definable
If we set "definable" = computable (e.g. constrain 0/1 sequences to the computable 0/1 sequences) then the required predicate must be computable.
--
William Hughes
WM
2017-04-19 16:11:38 UTC
Raw Message
Post by w***@gmail.com
Post by WM
Post by w***@gmail.com
Recall, any *subset* of words must be countable. However, it may not be true
that a subcollection of words must be a subset (E.g. If every subset of integers, equivalently every potentially infinite 0/1 sequence, must be computable then the indexes of the halting Turning machines form a subcollection but not a subset). The f's are s subcollection but not a subset.
If you have a countable set S, then every subcollection T is countable and is a set. This is provable by the Axiom of separation. The required predicate is definable
If we set "definable" = computable (e.g. constrain 0/1 sequences to the computable 0/1 sequences) then the required predicate must be computable.
Usually we do not put definable = computable, at least I never do so. For instance I can define the largest prime number or the smallest positive real number but cannot compute it.

When we talk about such objects, then we know what is meant. Therefore they are defined objects although not existing in mathematics.

Regards, WM
b***@gmail.com
2017-04-19 16:32:05 UTC
Raw Message
FOL doesn't care whether objects are defined or not. It
assume a universe of discourse U. What you do with FOL
you then define prediates. In set theory the only
predicate, if you don't add further predicates,

is the set membership, can be denoted by the "element
of" sign ∈ . So ZFC is not a theory about objects really,
its a theory about the membership predicate ∈ . Nevertheless
ZFC postulates with the help of the membership predicate

∈ here and then the existence of objects. But this is not
a postulation on the basis of definedness. There is no such
notion in FOL. The postulation is solely done by an existential
sentence and by postulating that there is some object with

a certain property. I have observed in JG and now in WM very
often this confusion that logic works with definedness, or
definability directly sticking to some object. But the ingredient
to postulating existence is not the object but the relationships

or functions that are used to postulate the existence. The object
must then appear in the domain or range of these functions,
or in the extend of the relationship, or in the complement of the
extend of the relationship. The relative complement to the universe

of discourse. Take for example the empty set, and the very simple
postulation of its existence:

exists x forall y (~ y ∈ x)

We see to make this axiom true, models have to be select ednot with
respect that something is contained in the relationship ∈ . Since
the empty set will at least not appear on the right hand side of the
relationship ∈ . It rather forces models of the theory to contain

the empty set in the universe of discourse. Thats all that happens.
The empty set itself doesn't receive some particular definedness
status. Well we can prove from the axiom directly its existence. And
using other axioms, like the extensionality axiom, we can show that

it is unique. But in the language of ZFC there is no "defined".
So the empty set has no special mark beyond how it acts inside
the membership ∈ . Which isn't even a property of the empty set itself
but of the extend of the membership ∈ , how this predicate forms

itself. So definedness is something that belongs to the fairy land,
Where the princess sits before the mirror and asks "Spieglein,
Spieglein an der Wand, Wer ist die Schönste im ganzen Land?« (*). But
in FOL no single object asks for definedness.

(*)
http://gutenberg.spiegel.de/buch/-6248/150
Post by WM
Post by w***@gmail.com
Post by WM
Post by w***@gmail.com
Recall, any *subset* of words must be countable. However, it may not be true
that a subcollection of words must be a subset (E.g. If every subset of integers, equivalently every potentially infinite 0/1 sequence, must be computable then the indexes of the halting Turning machines form a subcollection but not a subset). The f's are s subcollection but not a subset.
If you have a countable set S, then every subcollection T is countable and is a set. This is provable by the Axiom of separation. The required predicate is definable
If we set "definable" = computable (e.g. constrain 0/1 sequences to the computable 0/1 sequences) then the required predicate must be computable.
Usually we do not put definable = computable, at least I never do so. For instance I can define the largest prime number or the smallest positive real number but cannot compute it.
When we talk about such objects, then we know what is meant. Therefore they are defined objects although not existing in mathematics.
Regards, WM
b***@gmail.com
2017-04-19 16:40:13 UTC
Raw Message
Its the same for Peano. Peano is not about some
natural number definedness. Basically it only cares
about equality (=) and success S and zero 0. What it
defines the first predicate and the later two functions.

The universe of discourse is practically immaterial.
You can use sticks, stones, propeller heads what ever
you want for these objects. Also the language of Peano
contains no "definedness".

All that counts is that S works as desired and that zero
0 works as desired and that equality works as desired.
It helps to visualize the signature of a model. Signature(*)
is a notion from logic and model theory. It lists the

relationships and functions of a model. Here are
the signature of ZFC (using V for the universe
of discourse) and Peano (using N for the universe
of discourse):

ZFC:
= : V x V
∈ : V x V

Peano:
= : N x N
S : N -> N
0 : N

So the theories ZFC and Peano restrain these relations
and functions, but not really some "definedness"
of objects. These signatures are relatively simple, they
are even not multi-sorted.

(*)
https://en.wikipedia.org/wiki/Signature_%28logic%29
b***@gmail.com
2017-04-19 16:59:11 UTC
Raw Message
Hi,

Since "definedness" doesn't stick to an object, the
same holds for "computability". Take the number 3.
It can be the result of computable function. Or it
can be the result of a definable function.

So if you want to build theories about recursion
or complexity, you cannot pin point this via the
objects. For numbers they ca be sticks, stones,

You need to extend the signature. The easiest
extension which works quite far, in recursion theory
is gödelisation of a function. You can view it as
a higher order signature:

Recursion Theory:
{} : N -> (N -> N)

Or as a normal FOL signature:

Recursion Theory:
{} : N x N -> N

What is the meaing of {}. Well the idea is that the
function sends a Gödel code n, to the function {n} that
the Gödel code represents. Sometimes this is also denoted
by { φ i } i ∈ N, i.e. seen as a collection of numbered functions.

Only when the signatur is extended, by this new vocabulary
utility, it is facilated to talk about computation. If the
vocabulary is not extended, and if one tries to pin point
computability versus definedness at the objects,

one is very likely to run in circles for ever, since FOL
only offers to possibility to define relationships and
functions, and then to postulate some existence via axioms,
but there is no intrinsic "definednes" of objects.

Lets look what can be done with {}.
One example is the Snm theorem:

https://de.wikipedia.org/wiki/Smn-Theorem

It uses the {}, the English Wikipedia page is a little shorter.

Bye
Post by b***@gmail.com
= : V x V
∈ : V x V
= : N x N
S : N -> N
0 : N
b***@gmail.com
2017-04-19 17:11:46 UTC
Raw Message
Disclaimer: Of course you can try to do Peano inside
ZFC, or Recursion Theory inside ZFC, but this is very
complicated and I guess not the aim of ZFC, although
I have seen Dan doing such things in DC proof.

Sorry for the pun, but one never knows about the
expectations about ZFC. Better lower the expectations.
WM
2017-04-20 11:16:06 UTC
Raw Message
Post by b***@gmail.com
Its the same for Peano. Peano is not about some
natural number definedness. Basically it only cares
about equality (=) and success S and zero 0.
I see. Equality is particularly important and easily provable for undefined elements.

Regards, WM
Ross A. Finlayson
2017-04-20 02:10:31 UTC
Raw Message
Post by b***@gmail.com
FOL doesn't care whether objects are defined or not. It
assume a universe of discourse U. What you do with FOL
you then define prediates. In set theory the only
predicate, if you don't add further predicates,
is the set membership, can be denoted by the "element
of" sign ∈ . So ZFC is not a theory about objects really,
its a theory about the membership predicate ∈ . Nevertheless
ZFC postulates with the help of the membership predicate
∈ here and then the existence of objects. But this is not
a postulation on the basis of definedness. There is no such
notion in FOL. The postulation is solely done by an existential
sentence and by postulating that there is some object with
a certain property. I have observed in JG and now in WM very
often this confusion that logic works with definedness, or
definability directly sticking to some object. But the ingredient
to postulating existence is not the object but the relationships
or functions that are used to postulate the existence. The object
must then appear in the domain or range of these functions,
or in the extend of the relationship, or in the complement of the
extend of the relationship. The relative complement to the universe
of discourse. Take for example the empty set, and the very simple
exists x forall y (~ y ∈ x)
We see to make this axiom true, models have to be select ednot with
respect that something is contained in the relationship ∈ . Since
the empty set will at least not appear on the right hand side of the
relationship ∈ . It rather forces models of the theory to contain
the empty set in the universe of discourse. Thats all that happens.
The empty set itself doesn't receive some particular definedness
status. Well we can prove from the axiom directly its existence. And
using other axioms, like the extensionality axiom, we can show that
it is unique. But in the language of ZFC there is no "defined".
So the empty set has no special mark beyond how it acts inside
the membership ∈ . Which isn't even a property of the empty set itself
but of the extend of the membership ∈ , how this predicate forms
itself. So definedness is something that belongs to the fairy land,
Where the princess sits before the mirror and asks "Spieglein,
Spieglein an der Wand, Wer ist die Schönste im ganzen Land?« (*). But
in FOL no single object asks for definedness.
(*)
http://gutenberg.spiegel.de/buch/-6248/150
Post by WM
Post by w***@gmail.com
Post by WM
Post by w***@gmail.com
Recall, any *subset* of words must be countable. However, it may not be true
that a subcollection of words must be a subset (E.g. If every subset of integers, equivalently every potentially infinite 0/1 sequence, must be computable then the indexes of the halting Turning machines form a subcollection but not a subset). The f's are s subcollection but not a subset.
If you have a countable set S, then every subcollection T is countable and is a set. This is provable by the Axiom of separation. The required predicate is definable
If we set "definable" = computable (e.g. constrain 0/1 sequences to the computable 0/1 sequences) then the required predicate must be computable.
Usually we do not put definable = computable, at least I never do so. For instance I can define the largest prime number or the smallest positive real number but cannot compute it.
When we talk about such objects, then we know what is meant. Therefore they are defined objects although not existing in mathematics.
Regards, WM
The empty set and omega set are constants in ZFC,
they're defined terms.

You should well recall recent discussions of axiomatizations
of the natural integers as so simple and as of objects in the
same language and the resulting grounds and bases for induction
as follow the regular constants, where both share the empty set
in its ordinal assignment as zero, that ZF's feature as a set
theory is its omega set, which is a regular well-founded set,
which is actually a _restriction_ of comprehension, where all
the other axioms than Infinity and Regularity are _expansions_
of comprehension. Infinity the axiom is a _restriction_ of
comprehension because it's well-founded a.k.a. regular a.k.a.
ordinary, which Russell advises is at best an incomplete
caricature of omega the ordinary and extra-ordinary set.

Then, various strong platonists have those exist, too,
and not just as their abstract forms, which they are,
but also as of all things that are of those things
(which they are).
WM
2017-04-20 11:16:20 UTC
Raw Message
Post by b***@gmail.com
But
in FOL no single object asks for definedness.
Objects are defined already or they are not objects. At least in mathematics this is the case.

Regards, WM
e***@arcor.de
2017-04-20 14:16:53 UTC
Raw Message
Post by WM
Post by b***@gmail.com
But
in FOL no single object asks for definedness.
Objects are defined already or they are not objects. At least in mathematics this is the case.
Regards, WM
What about quantum mechanics? I guess, Robert McEachern needs support,
see what I wrote in "Wallis, Leibniz, Bernoulli, and ongoing confusion".
WM
2017-04-20 15:32:13 UTC
Raw Message
Post by e***@arcor.de
Post by WM
Post by b***@gmail.com
But
in FOL no single object asks for definedness.
Objects are defined already or they are not objects. At least in mathematics this is the case.
Hi Eckard!

My statement concerns objects of mathematics or, more general, creations of the mind. Physical objects exist independently of whether we know them.

REgards, WM
e***@arcor.de
2017-04-20 20:45:14 UTC
Raw Message
Post by WM
Post by e***@arcor.de
Post by WM
Objects are defined already or they are not objects. At least in mathematics this is the case.
Hi Eckard!
My statement concerns objects of mathematics or, more general, creations of the mind. Physical objects exist independently of whether we know them.
Hi WM,

Feynman's (in)famous utterance "shut up and calculate" might
illustrate to what extent quantum theories including their paradoxes
are creations of the mind too.

Bell's inequality has been considered an evidence for decades.
McEachern shows that it can be classically explained.
You will be surprized.
By the way, my "Wallis, ..." largely supports Bassam K K's criticism
of the mathematical infinity. Wikipedia shows how counter-reasonable
the hyperreals are. Leibniz and Bernoulli were masters of Faihinger's as if.

Regards, Eckard
WM
2017-04-21 15:54:55 UTC
Raw Message
Post by e***@arcor.de
Bell's inequality has been considered an evidence for decades.
McEachern shows that it can be classically explained.
You will be surprized.
I doubt that. The simplest proof for entanglement does not need Bell's inequalities. I have for decades explained that stuff to my students by crossed polarizers P1 and P2:

P1 photon1 Source photon2 P2

According to Malus' law the average probability for simultaneous transmission of both photons is not zero - contrary to fact.
Post by e***@arcor.de
By the way, my "Wallis, ..." largely supports Bassam K K's criticism
of the mathematical infinity.
That is a reasonable opinion. Therefore my https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf contains statements of both of you. Where is your Wallis ... available?

Regards, WM
Python
2017-04-21 20:20:31 UTC
Raw Message
Post by WM
Post by e***@arcor.de
Bell's inequality has been considered an evidence for decades.
McEachern shows that it can be classically explained.
You will be surprized.
I doubt that. The simplest proof for entanglement does not need Bell's inequalities.
Thanks to confirm that as a teacher you didn't only shit on mathematics,
but on physics too. There were little doubt, but few evidences.
e***@arcor.de
2017-04-22 06:14:50 UTC
Raw Message
Post by WM
Post by e***@arcor.de
Bell's inequality has been considered an evidence for decades.
McEachern shows that it can be classically explained.
You will be surprized.
P1 photon1 Source photon2 P2
According to Malus' law the average probability for simultaneous transmission of both photons is not zero - contrary to fact.
Post by e***@arcor.de
By the way, my "Wallis, ..." largely supports Bassam K K's criticism
of the mathematical infinity.
That is a reasonable opinion. Therefore my https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf contains statements of both of you. Where is your Wallis ... available?
Regards, WM
"Wallis ..." is available here at 19, April:

For McEachern see for instance
viXra.org/abs/1609.0129
The discussion mentions infinity.

Many of Rob's surprizing arguments can be found at FQXi.org blogs,
for instance: The double slit experiment doesn't relate to the
property of photon but to the property of the double slit.

Does science really need moderators like van Hees?

Regards,
Eckard
John Gabriel
2017-04-20 14:24:41 UTC
Raw Message
Post by WM
Post by b***@gmail.com
But
in FOL no single object asks for definedness.
Objects are defined already or they are not objects. At least in mathematics this is the case.
Chuckle. FOL stands for the first three letters of the word FOLLY in mythmatics. Funny how morons parrot everything they learn and think that makes them smart...
Post by WM
Regards, WM
WM
2017-04-20 15:40:16 UTC
Raw Message
Post by John Gabriel
Chuckle. FOL stands for the first three letters of the word FOLLY in mythmatics. Funny how morons parrot everything they learn and think that makes them smart...
In fact, it is really painful to see how a culture of nonsense grows profusely in mathematical institutes, in particular in "logic" departments. But without undefinable definitions, unthinkable thoughts, unreal real numbers set theory breaks down. Recently I documented a very enlightening discussion on that topic here: "Comments on undefinable mathematics and unusable languages", p. 303ff of https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf

Regards, WM
bassam king karzeddin
2017-04-20 16:08:52 UTC
Raw Message
Post by WM
Post by John Gabriel
Chuckle. FOL stands for the first three letters of the word FOLLY in mythmatics. Funny how morons parrot everything they learn and think that makes them smart...
In fact, it is really painful to see how a culture of nonsense grows profusely in mathematical institutes, in particular in "logic" departments. But without undefinable definitions, unthinkable thoughts, unreal real numbers set theory breaks down. Recently I documented a very enlightening discussion on that topic here: "Comments on undefinable mathematics and unusable languages", p. 303ff of https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf
Regards, WM
Congratulation

I hardly made a fast glimpse throughout its chapters, it seems mostly against wrong inherited mathematical concepts i.e (fighting the ignorance in modern mathematics) that are very important subjects for sure

My regards
BK
w***@gmail.com
2017-04-19 19:06:56 UTC
Raw Message
Post by WM
Post by w***@gmail.com
Post by WM
Post by w***@gmail.com
Recall, any *subset* of words must be countable. However, it may not be true
that a subcollection of words must be a subset (E.g. If every subset of integers, equivalently every potentially infinite 0/1 sequence, must be computable then the indexes of the halting Turning machines form a subcollection but not a subset). The f's are s subcollection but not a subset.
If you have a countable set S, then every subcollection T is countable and is a set. This is provable by the Axiom of separation. The required predicate is definable
If we set "definable" = computable (e.g. constrain 0/1 sequences to the computable 0/1 sequences) then the required predicate must be computable.
Usually we do not put definable = computable,
The problem is that if you are not very careful with the concept of "definable" you run into Richard's paradox and a theory in which all statements are true.
Setting definable = computable avoids Richard's paradox which is why I use it for examples.
--
William Hughes
WM
2017-04-20 11:15:40 UTC
Raw Message
Post by w***@gmail.com
Post by WM
Post by w***@gmail.com
If we set "definable" = computable (e.g. constrain 0/1 sequences to the computable 0/1 sequences) then the required predicate must be computable.
Usually we do not put definable = computable,
The problem is that if you are not very careful with the concept of "definable" you run into Richard's paradox and a theory in which all statements are true.
Setting definable = computable avoids Richard's paradox which is why I use it for examples.
There are many paradoxes which are based on logic and have nothing to do with set theory. Take Socrates' I know that I no nothing or Berry's paradox:

If all definitions of numbers with less than 100 letters already are given, then also the sequence of letters Z = "the least number which cannot be defined by less than 100 letters" does define a number. As an example, let a = 01, b = 02, c = 03 etc. By "example" we have defined the number example = 05240113161205 and also the sequence Z would already define a number. Only by the change of language from numeral to colloquial the apparent paradox occurs.

Regards, WM
w***@gmail.com
2017-04-20 20:34:54 UTC
Raw Message
On Thursday, April 20, 2017 at 8:15:46 AM UTC-3, WM wrote:
<snip>
Post by WM
If all definitions of numbers with less than 100 letters already are given, then also the sequence of letters Z = "the least number which cannot be defined by less than 100 letters" does define a number.
A rather big if. Lets try to do it. Put down a number for every sequence of
less than one hundred characters. Some things are easy like "the number 15", 15, or "the smallest prime greater than 7", 11, or "10 * 5 * 103", 5150. Sequences like " a horse" or "xx&* **@(a\$" or "the smallest even prime greater than 2" do not define numbers. Sooner or later we will come to "The smallest Z that cannot be defined in 100 characters". What do we put down? We cannot put anything down without finishing, and we cannot finish without putting something down. So does the sequences define a number? Richard's paradox (this is just another form) is not just a paradox caused by the use of colloquial language.
--
William Hughes
WM
2017-04-21 15:56:05 UTC
Raw Message
Post by w***@gmail.com
<snip>
Post by WM
If all definitions of numbers with less than 100 letters already are given, then also the sequence of letters Z = "the least number which cannot be defined by less than 100 letters" does define a number.
A rather big if. Lets try to do it.
You have overlooked my example. Here it is again: As an example, let a = 01, b = 02, c = 03 etc. By "example" we have defined the number example = 05240113161205 and also the sequence Z would already define a number.

In this formalism Richard's sequence defines the number Z = 200801...

Regards, WM
Me
2017-04-21 06:21:55 UTC
Raw Message
Post by WM
I can define the largest prime number or the smallest positive real number
No, you can't, idiot.
Post by WM
but cannot compute [them].
Indeed, that's because THERE IS NO largest prime number and/or smallest positive real number, moron (so you cant't compute "them", because there ARE NO such numbers).

Mückenheim, you are too dumb to do ANY mathematics.
WM
2017-04-21 15:57:26 UTC
Raw Message
Post by Me
Post by WM
I can define the largest prime number or the smallest positive real number
No, you can't,
Let L be the largest prime number.
Let SPQR be the smallest positive real number.
That was easy.
Post by Me
Post by WM
but cannot compute [them].
Indeed, that's because THERE IS NO largest prime number and/or smallest positive real number,
Na und?

There is no devil.
Define:
Let D be the devil.
Or
Let FF be an intelligent person.

Everything is possible.

Regards, WM
Me
2017-04-21 16:04:39 UTC
Raw Message
Post by WM
Post by Me
Post by WM
I can define the largest prime number or the smallest positive real number
No, you can't,
Let L be the largest prime number.
Let SPQR be the smallest positive real number.
That was easy.
Yeah, certainly, for an idiot.
Post by WM
Everything is possible.
Sure! In Muckenmatics. :-)
f***@gmail.com
2017-04-21 23:45:41 UTC
Raw Message
Post by Me
Post by WM
Post by Me
Post by WM
I can define the largest prime number or the smallest positive real number
No, you can't,
Let L be the largest prime number.
Let SPQR be the smallest positive real number.
That was easy.
Yeah, certainly, for an idiot.
Actually, the following article comes to mind:

Unskilled and unaware of it: How difficulties in recognizing one's own incompetence lead to inflated self-assessments.

By Kruger, Justin; Dunning, David

Python
2017-04-21 20:00:29 UTC
Raw Message
Post by WM
Post by Me
Post by WM
I can define the largest prime number or the smallest positive real number
No, you can't,
Let L be the largest prime number.
Let SPQR be the smallest positive real number.
Senatus PopulusQue Romanus?!
Post by WM
Everything is possible.
Yes, even the worse. You are a living evidence of that.
FredJeffries
2017-04-27 16:07:30 UTC
Raw Message
Post by WM
Post by Me
Post by WM
I can define the largest prime number or the smallest positive real number
No, you can't,
Let L be the largest prime number.
Let SPQR be the smallest positive real number.
That was easy.
Post by Me
Post by WM
but cannot compute [them].
Indeed, that's because THERE IS NO largest prime number and/or smallest positive real number,
Na und?
There is no devil.
Let D be the devil.
Or
Let FF be an intelligent person.
Everything is possible.
Our esteemed professor reveals not only his ignorance of the concept of 'definition' but also of the difference between definite and indefinite articles.

One can define the notion of 'A largest prime number' something like:
A prime number p is a largest prime number if for all prime numbers q, p >= q

But to sensibly talk about THE largest prime number one must SHOW that there is one and only one prime number satisfying the definition of 'a largest prime number'.
e***@arcor.de
2017-05-04 03:56:46 UTC
Raw Message
Post by FredJeffries
But to sensibly talk about THE largest prime number one must SHOW that there is one and only one prime number satisfying the definition of 'a largest prime number'.
Or one must be equipped with the brutal freedom of mathematics for being rigorous.
Ross A. Finlayson
2017-05-04 04:50:13 UTC
Raw Message
Post by e***@arcor.de
Post by FredJeffries
But to sensibly talk about THE largest prime number one must SHOW that there is one and only one prime number satisfying the definition of 'a largest prime number'.
Or one must be equipped with the brutal freedom of mathematics for being rigorous.
Mathematics is perfect.

Mathematics surpasses the usual regular logical paradoxes,
and is perfect.

So, if mathematical infinity is beyond comprehension
then that's just weakness.

Now, you might be thinking of large finite systems
with a prime on top or for example a composite on top,
and number theorists have this as a notion also for "a"
or "the" points at infinity (and at various infinities).

Mathematics _owes_ physics logically sound mathematical
infinities (and for applications, directly, and to
explain the effects of values in numbers, for physics).
e***@arcor.de
2017-05-04 14:19:06 UTC
Raw Message
Post by Ross A. Finlayson
Post by FredJeffries
But to sensibly talk about THE largest prime number one must SHOW that there is one and only one prime number satisfying the definition of 'a largest prime number'.
So, if mathematical infinity is beyond comprehension
then that's just weakness.
Mathematical infinity is a relative infinity as described by Leibniz:
- larger than every other nameable quantity:
He explained: every number is finite and can be named.
The infinities and infinitesimals are fictions with a fundamentum in re.

I cannot see this beyound comprehension. However, the relative infinity
(Katz called it B-continuum from Bernoulli) must not be equated with the logical property of being endless which was used by Galileo Galilei who let Salviati say
the relations larger than, equal to, and smaller than do not belong to infinite quantities, just to what we today are calling the rationals. This implies that
in contrast to Dedekind/Cantor mathematics, there is a genuine continuum of truly real numbers.

Such simple clarification is definitely not beyond comprehension unless one feels obliged to understand it in the context of mandatory tenets.
Post by Ross A. Finlayson
Now, you might be thinking of large finite systems
with a prime on top or for example a composite on top,
and number theorists have this as a notion also for "a"
or "the" points at infinity (and at various infinities).
Well, the relative infinity lets room for a lot of naive Cantorian whishful thinking up to transfinite, hyperreal and surreal numbers.
If these construct did have practical relevance, this was indeed beyond comprehension.
Post by Ross A. Finlayson
Mathematics _owes_ physics logically sound mathematical
infinities (and for applications, directly, and to
explain the effects of values in numbers, for physics).
Can you tell some not just claimed applications?

I am offering three counterexamples:
- Buridan's donkey
- integral tables give for the integral from 0 to 00 over dx (sin x cos x)/x
besides two reasonable solutions pi/2 for |x|<1 and 0 for |x|>1 a third value pi/4 for |x| = 1 which is useless and misleading
- actually claimed but unrealistic physical singularities
Ross A. Finlayson
2017-05-05 01:25:02 UTC
Raw Message
Post by e***@arcor.de
Post by Ross A. Finlayson
Post by FredJeffries
But to sensibly talk about THE largest prime number one must SHOW that there is one and only one prime number satisfying the definition of 'a largest prime number'.
So, if mathematical infinity is beyond comprehension
then that's just weakness.
He explained: every number is finite and can be named.
The infinities and infinitesimals are fictions with a fundamentum in re.
I cannot see this beyound comprehension. However, the relative infinity
(Katz called it B-continuum from Bernoulli) must not be equated with the logical property of being endless which was used by Galileo Galilei who let Salviati say
the relations larger than, equal to, and smaller than do not belong to infinite quantities, just to what we today are calling the rationals. This implies that
in contrast to Dedekind/Cantor mathematics, there is a genuine continuum of truly real numbers.
Such simple clarification is definitely not beyond comprehension unless one feels obliged to understand it in the context of mandatory tenets.
Post by Ross A. Finlayson
Now, you might be thinking of large finite systems
with a prime on top or for example a composite on top,
and number theorists have this as a notion also for "a"
or "the" points at infinity (and at various infinities).
Well, the relative infinity lets room for a lot of naive Cantorian whishful thinking up to transfinite, hyperreal and surreal numbers.
If these construct did have practical relevance, this was indeed beyond comprehension.
Post by Ross A. Finlayson
Mathematics _owes_ physics logically sound mathematical
infinities (and for applications, directly, and to
explain the effects of values in numbers, for physics).
Can you tell some not just claimed applications?
- Buridan's donkey
- integral tables give for the integral from 0 to 00 over dx (sin x cos x)/x
besides two reasonable solutions pi/2 for |x|<1 and 0 for |x|>1 a third value pi/4 for |x| = 1 which is useless and misleading
- actually claimed but unrealistic physical singularities
Applications? Path integral, rolled up in physics
as "non-Newtonian dynamics" (including Einsteinian
dynamics).

Something like Euler's identity with the constants
together or Sum n ~= -1/12 is an example of a similar
notion as the principal root of a real number, that
then besides the negative root are all these many
complex then hypercomplex roots. These are in extensions
that until discovered wouldn't add up (or rather, down).

Physics does have quite a few singularities (or infinities),
as well systems in dynamics with "infinite degrees of
freedom" (infinities), as well there are effects in the
discretization, or quantum, as of the continuum, or field,

mathematics: discrete <-> continuous
physics: quantum <-> field

that really are about those objects as infinitesimals
in the mathematics or continua in the mathematics
about then that discretization is not a reversible
result, in the mathematics, on the real objects,
themselves, mathematically.

Mathematics and physics have pretty much the same

Anyways, there is available the scientific experiment
or the data that these days (contra antiquity) the
physics must deliver a model for all the physics,
there is that a "unified" model is required for the
theoretical physics, and with the effects together
or of the whole, the applied physics.
e***@arcor.de
2017-05-05 09:52:30 UTC
Raw Message
Post by Ross A. Finlayson
Post by e***@arcor.de
I cannot see this beyound comprehension. However, the relative infinity
(Katz called it B-continuum from Bernoulli) must not be equated with the logical property of being endless which was used by Galileo Galilei who let Salviati say
the relations larger than, equal to, and smaller than do not belong to infinite quantities, just to what we today are calling the rationals. This implies that
in contrast to Dedekind/Cantor mathematics, there is a genuine continuum of truly real numbers.
Such simple clarification is definitely not beyond comprehension unless one feels obliged to understand it in the context of mandatory tenets.
Post by Ross A. Finlayson
Now, you might be thinking of large finite systems
with a prime on top or for example a composite on top,
and number theorists have this as a notion also for "a"
or "the" points at infinity (and at various infinities).
Well, the relative infinity lets room for a lot of naive Cantorian whishful thinking up to transfinite, hyperreal and surreal numbers.
If these construct did have practical relevance, this was indeed beyond comprehension.
Post by Ross A. Finlayson
Mathematics _owes_ physics logically sound mathematical
infinities (and for applications, directly, and to
explain the effects of values in numbers, for physics).
Can you tell some not just claimed applications?
- Buridan's donkey
- integral tables give for the integral from 0 to 00 over dx (sin x cos x)/x
besides two reasonable solutions pi/2 for |x|<1 and 0 for |x|>1 a third value pi/4 for |x| = 1 which is useless and misleading
- actually claimed but unrealistic physical singularities
Applications? Path integral, rolled up in physics
as "non-Newtonian dynamics" (including Einsteinian
dynamics).
I cannot see Non-Newtonian an example for relative infinities.
BTW, MOND and non-Newtonian viscosity refer to different subjects.
Einstein's 1905 electrodynamics of moving bodies assumes ideal
continuity as defined by Peirce.
Post by Ross A. Finlayson
Something like Euler's identity
exp(i pi) may be considered as the limit of a completely
(not just relative infinite) sum.

with the constants
Post by Ross A. Finlayson
together or Sum n ~= -1/12 is an example of a similar
notion as the principal root of a real number, that
then besides the negative root are all these many
complex then hypercomplex roots.
Admittedly, I am not a fan of Clifford algebra.
I even admit being not firm in terminology unital, unitary, etc.
Therefore I will perhaps not grasp what you mean here.

These are in extensions
Post by Ross A. Finlayson
that until discovered wouldn't add up (or rather, down).
Physics does have quite a few singularities (or infinities),
as well systems in dynamics with "infinite degrees of
freedom" (infinities), as well there are effects in the
discretization, or quantum, as of the continuum, or field,
My Galilean (A-) notion of infinity ascribes the property
to be endless to just one quantity. Different quantities
may of course be or not be endless, independent from each other.

So far, there is no evidence for unlimited divisibility in physics.
This doesn't imply that Euclid's and Peirce's concepts of point
and continuum, respectively, are wrong.
Post by Ross A. Finlayson
mathematics: discrete <-> continuous
physics: quantum <-> field
that really are about those objects as infinitesimals
in the mathematics or continua in the mathematics
Infinitesimal means smaller than anything, in other words relative
and actually in some sense discrete i.e. finite, not yet infinite.
What about quantum, I would appreciate if someone was ready to disprove
McEachern.
Ross A. Finlayson
2017-05-05 23:45:01 UTC
Raw Message
Post by e***@arcor.de
Post by Ross A. Finlayson
Post by e***@arcor.de
I cannot see this beyound comprehension. However, the relative infinity
(Katz called it B-continuum from Bernoulli) must not be equated with the logical property of being endless which was used by Galileo Galilei who let Salviati say
the relations larger than, equal to, and smaller than do not belong to infinite quantities, just to what we today are calling the rationals. This implies that
in contrast to Dedekind/Cantor mathematics, there is a genuine continuum of truly real numbers.
Such simple clarification is definitely not beyond comprehension unless one feels obliged to understand it in the context of mandatory tenets.
Post by Ross A. Finlayson
Now, you might be thinking of large finite systems
with a prime on top or for example a composite on top,
and number theorists have this as a notion also for "a"
or "the" points at infinity (and at various infinities).
Well, the relative infinity lets room for a lot of naive Cantorian whishful thinking up to transfinite, hyperreal and surreal numbers.
If these construct did have practical relevance, this was indeed beyond comprehension.
Post by Ross A. Finlayson
Mathematics _owes_ physics logically sound mathematical
infinities (and for applications, directly, and to
explain the effects of values in numbers, for physics).
Can you tell some not just claimed applications?
- Buridan's donkey
- integral tables give for the integral from 0 to 00 over dx (sin x cos x)/x
besides two reasonable solutions pi/2 for |x|<1 and 0 for |x|>1 a third value pi/4 for |x| = 1 which is useless and misleading
- actually claimed but unrealistic physical singularities
Applications? Path integral, rolled up in physics
as "non-Newtonian dynamics" (including Einsteinian
dynamics).
I cannot see Non-Newtonian an example for relative infinities.
BTW, MOND and non-Newtonian viscosity refer to different subjects.
Einstein's 1905 electrodynamics of moving bodies assumes ideal
continuity as defined by Peirce.
Post by Ross A. Finlayson
Something like Euler's identity
exp(i pi) may be considered as the limit of a completely
(not just relative infinite) sum.
with the constants
Post by Ross A. Finlayson
together or Sum n ~= -1/12 is an example of a similar
notion as the principal root of a real number, that
then besides the negative root are all these many
complex then hypercomplex roots.
Admittedly, I am not a fan of Clifford algebra.
I even admit being not firm in terminology unital, unitary, etc.
Therefore I will perhaps not grasp what you mean here.
These are in extensions
Post by Ross A. Finlayson
that until discovered wouldn't add up (or rather, down).
Physics does have quite a few singularities (or infinities),
as well systems in dynamics with "infinite degrees of
freedom" (infinities), as well there are effects in the
discretization, or quantum, as of the continuum, or field,
My Galilean (A-) notion of infinity ascribes the property
to be endless to just one quantity. Different quantities
may of course be or not be endless, independent from each other.
So far, there is no evidence for unlimited divisibility in physics.
This doesn't imply that Euclid's and Peirce's concepts of point
and continuum, respectively, are wrong.
Post by Ross A. Finlayson
mathematics: discrete <-> continuous
physics: quantum <-> field
that really are about those objects as infinitesimals
in the mathematics or continua in the mathematics
Infinitesimal means smaller than anything, in other words relative
and actually in some sense discrete i.e. finite, not yet infinite.
What about quantum, I would appreciate if someone was ready to disprove
McEachern.
Basically that's about the path integral and where
sum-of-histories is the path integral and physics
fudges it to be 1.0 (about how it vanishes on
measurement about the measurement and observer
effects and here the super-classical wave model
of the tachyonic/bradyonic pilot wave the collapses
and reforms as from being particulate or an interaction).

Similarly Einstein's mc^2 is just the first term of
a series expansion for a formula for kinetic energy,
it's "extra-Einsteinian" this more "non-Newtonian"
but the mentioned "infinite functional degrees" of
the following terms aren't exactly sensical to the
usual classical and linear.

Clearly this is obvious if you've followed Einstein's
derivation of E (as mc^2).

Then, about the universe really being infinite, you
should know that over time, the universe is found
bigger and older. You can basically chart the
experiment of all the collected cosmological experimens
and the more you look, the bigger it gets.

The complement in the small is quite symmetrical:
the more closely (sub-)atomic particles are
examined, the smaller they get.

Those are infinities (or an infinity) and infinitesimals
(or a point).

So, you don't need that to compute rise/run, which is
rise/run, and otherwise parameterize the classical, which
is of course simple and classical and linear. But, in
terms of the "bigger picture" as it were, these are
extra- (or super-)classical parts of physics and plainly
that's the direction for real progress in fundamental
physics.

That's "super", not "dumber", and of course, then,
eventually it's also "simpler", re simpliciter.
e***@arcor.de
2017-05-06 02:34:50 UTC
Raw Message
Post by Ross A. Finlayson
Post by e***@arcor.de
Post by e***@arcor.de
I cannot see this beyound comprehension. However, the relative infinity
(Katz called it B-continuum from Bernoulli) must not be equated with the > > > > logical property of being endless which was used by Galileo Galilei who > > > > let Salviati say
the relations larger than, equal to, and smaller than do not belong to
infinite quantities, just to what we today are calling the rationals.
This implies that
in contrast to Dedekind/Cantor mathematics, there is a genuine continuum > > > > of truly real numbers.
- Buridan's donkey
- integral tables give for the integral from 0 to 00
over dx (sin x cos x)/x
besides two reasonable solutions pi/2 for |x|<1 and 0 for |x|>1
a third value pi/4 for |x| = 1 which is useless and misleading
- actually claimed but unrealistic physical singularities
I would like to add a lot, e.g. the pebble vs. point issue and
Cantor's treatment of the non-distinguishable as distinct.
Post by Ross A. Finlayson
Post by e***@arcor.de
exp(i pi) may be considered as the limit of a completely
(not just relative infinite) sum.
Infinitesimal means smaller than anything, in other words relative
and actually in some sense discrete i.e. finite, not yet infinite.
What about quantum, I would appreciate if someone was ready to disprove
McEachern.
Basically that's about the path integral and where
sum-of-histories is the path integral and physics
fudges it to be 1.0 (about how it vanishes on
measurement about the measurement and observer
effects and here the super-classical wave model
of the tachyonic/bradyonic pilot wave the collapses
and reforms as from being particulate or an interaction).
I am not sure whether you refer here to McEachern.
Post by Ross A. Finlayson
Similarly Einstein's mc^2 is just the first term of
a series expansion for a formula for kinetic energy,
Series expansions are NOT just B-infinite.
Post by Ross A. Finlayson
Then, about the universe really being infinite, you
should know that over time, the universe is found
bigger and older. You can basically chart the
experiment of all the collected cosmological experimens
and the more you look, the bigger it gets.
Perhaps I should be cautious and not reveal my own guess
that there might indeed be reasons to question the BB etc.
Post by Ross A. Finlayson
the more closely (sub-)atomic particles are
examined, the smaller they get.
Let me stress again Galileo Galilei's insight:
The property of being endless does NOT directly apply
to the relations smaller than, equal to, or larger than.

While the Catholic Church up to now denies that
G. is relevant as a mathematician, I see his
reasoning superior to present fudging.
I just learned this word from you. Thank you.
Post by Ross A. Finlayson
Those are infinities (or an infinity) and infinitesimals
(or a point).
Infinities and "an" infinity are relative.
Post by Ross A. Finlayson
So, you don't need that to compute rise/run, which is
rise/run, and otherwise parameterize the classical, which
is of course simple and classical and linear. But, in
terms of the "bigger picture" as it were, these are
extra- (or super-)classical parts of physics and plainly
that's the direction for real progress in fundamental
physics.
Sounds as if you didn't understand my (Galileo's) point:
A point is something that has no parts (Euclid).
b***@gmail.com
2017-05-05 10:57:50 UTC
Raw Message
There are like a dozen different infinities in math usage,
some months ago somebody posted a nice old link to a

sci.math post from 19xx , which listed some of them.
Sadly I am unable to find this post again so quickly.
Post by e***@arcor.de
Mathematical infinity
b***@gmail.com
2017-05-05 11:30:37 UTC
Raw Message
AP started his crank career when he posted "#2 book
"Correcting Present Day Mathematics..."; (1) Infinity
exists in one and only one form proof."

But lets check how different the discrete and the
continues are. Archimedes might have expressed the
ratio between the perfect circle circum U and the
perfect circle area A as:

2:R = U:A

/* correcting my previous post */

What about the n-gon, what do we get there? For the
n-gon we have the following, where R is the

U_n = 2*n*r*tan(pi/n)

A_n = n*r^2*tan(pi/n)

So we have this time again:

2:R = U_n:A_n

Isn't this amazing, no difference between
discrete and continues?

https://de.wikipedia.org/wiki/Regelm%C3%A4%C3%9Figes_Polygon#Umfang_und_Fl.C3.A4cheninhalt
Post by b***@gmail.com
There are like a dozen different infinities in math usage,
some months ago somebody posted a nice old link to a
sci.math post from 19xx , which listed some of them.
Sadly I am unable to find this post again so quickly.
Post by e***@arcor.de
Mathematical infinity
b***@gmail.com
2017-05-05 11:38:01 UTC
Raw Message
As free lunch we get. He He:

lim n->oo n*tan(pi/n) = pi

Want to build a physics without perfect circles,
maybe just use a different constant than pi. LoL
Post by b***@gmail.com
AP started his crank career when he posted "#2 book
"Correcting Present Day Mathematics..."; (1) Infinity
exists in one and only one form proof."
But lets check how different the discrete and the
continues are. Archimedes might have expressed the
ratio between the perfect circle circum U and the
2:R = U:A
/* correcting my previous post */
What about the n-gon, what do we get there? For the
n-gon we have the following, where R is the
U_n = 2*n*r*tan(pi/n)
A_n = n*r^2*tan(pi/n)
2:R = U_n:A_n
Isn't this amazing, no difference between
discrete and continues?
https://de.wikipedia.org/wiki/Regelm%C3%A4%C3%9Figes_Polygon#Umfang_und_Fl.C3.A4cheninhalt
Post by b***@gmail.com
There are like a dozen different infinities in math usage,
some months ago somebody posted a nice old link to a
sci.math post from 19xx , which listed some of them.
Sadly I am unable to find this post again so quickly.
Post by e***@arcor.de
Mathematical infinity
bassam king karzeddin
2017-04-15 16:36:32 UTC
Raw Message
Post by b***@gmail.com
So whats the difference between D = lim_n->oo D_n where
e = sqrt(2) - D
e <> 0
Is this the case for the reals or not. And if it is the case,
what is this e exactly? Do we have e^2 = 0?
Post by b***@gmail.com
Well D = 1.41421356237... is a limes its the same as your arithmo-
1
1 2
1 2 3
1 2 3 4
...
D is the limes of all chop chops D_n, i.e. D_1 = 1.4, D_2 =1.41, ..
etc.. I didnt ask for sqrt(2) <> D_n, everybody knows that
sqrt(2) <> D_n, because sqrt(2) is irrational.
Post by WM
Post by b***@gmail.com
So sqrt(2) = 1.41421356237... + e,
e depends on how many digits you use. But it can only be estimated, not calculated, because sqrt(2) has no decimal representation.
Example: In sqrt(2) = 1.4, e > 0.01421356237.
Regards, WM
Burr...

Had you ever asked your so selly self, what is the largest rational number that is less than sqrt(2),

Or similarly, Had you ever asked your so tiny self, what is the least rational number that is greater than sqrt(2),

Of course, it is more than trivial to see and confess openly that those (greatest, or least) rational numbers do not not exist, do they? wonder!

But why then you and the so broken mathematics insist that exist at infinity? wonder
And a Fool professional answer would say yes they exist at infinity, but infinity is not there moron (except in your toooo... tiny empty skull) and for sure
And how magically your rational decimal would turn suddenly irrational, after many billions of digits, after many billions of years, it would remain rational as long as you can count, but you can not count indefinitely for sure

Thus, you are after a clear illusion in your mind

And that does not mean in any case that sqrt(2) does not exist, or a symptom of a number as some famous idiots constantly say

Yes, sqrt(2), and sqrt(sqrt(2)), and generally [2^{2^{- n}}] do all exist exactly

for any + ve integer (n), and independently from rational numbers even that rational or decimal goes to

And guess what that positive integer (n) could be?

It can be for little explanation as large as we wish, I mean it can be as finite integer with sequence digits such that it can fill up trillions of galaxy size, where every trillion of sequence digits are stored only with one mm cube (imagine), but still rational, is not it?

And even much larger finite integers can be assumed for sure, because simply infinity IS NOT THERE EXCEPT IN EMPTY SKULLS, got it? wonder!

So, finite and infinite are not different, since you did not define the finite in order to define correctly the infinite

And may be the AP can teach you a better lesson in this regard

But, still you would not get anything out of this free lecture for sure

And it does not any matter

And the real difference of sqrt(2) and its decimal rational expansion is really unreal number, because your infinity is defined as unreal number

Regards
Bassam King Karzeddin
15th, April, 2017
bassam king karzeddin
2017-04-29 13:59:42 UTC
Raw Message
Post by bassam king karzeddin
Post by b***@gmail.com
So whats the difference between D = lim_n->oo D_n where
e = sqrt(2) - D
e <> 0
Is this the case for the reals or not. And if it is the case,
what is this e exactly? Do we have e^2 = 0?
Post by b***@gmail.com
Well D = 1.41421356237... is a limes its the same as your arithmo-
1
1 2
1 2 3
1 2 3 4
...
D is the limes of all chop chops D_n, i.e. D_1 = 1.4, D_2 =1.41, ..
etc.. I didnt ask for sqrt(2) <> D_n, everybody knows that
sqrt(2) <> D_n, because sqrt(2) is irrational.
Post by WM
Post by b***@gmail.com
So sqrt(2) = 1.41421356237... + e,
e depends on how many digits you use. But it can only be estimated, not calculated, because sqrt(2) has no decimal representation.
Example: In sqrt(2) = 1.4, e > 0.01421356237.
Regards, WM
Burr...
Had you ever asked your so selly self, what is the largest rational number that is less than sqrt(2),
Or similarly, Had you ever asked your so tiny self, what is the least rational number that is greater than sqrt(2),
Of course, it is more than trivial to see and confess openly that those (greatest, or least) rational numbers do not not exist, do they? wonder!
But why then you and the so broken mathematics insist that exist at infinity? wonder
And a Fool professional answer would say yes they exist at infinity, but infinity is not there moron (except in your toooo... tiny empty skull) and for sure
And how magically your rational decimal would turn suddenly irrational, after many billions of digits, after many billions of years, it would remain rational as long as you can count, but you can not count indefinitely for sure
Thus, you are after a clear illusion in your mind
And that does not mean in any case that sqrt(2) does not exist, or a symptom of a number as some famous idiots constantly say
Yes, sqrt(2), and sqrt(sqrt(2)), and generally [2^{2^{- n}}] do all exist exactly
for any + ve integer (n), and independently from rational numbers even that rational or decimal goes to
And guess what that positive integer (n) could be?
It can be for little explanation as large as we wish, I mean it can be as finite integer with sequence digits such that it can fill up trillions of galaxy size, where every trillion of sequence digits are stored only with one mm cube (imagine), but still rational, is not it?
And even much larger finite integers can be assumed for sure, because simply infinity IS NOT THERE EXCEPT IN EMPTY SKULLS, got it? wonder!
So, finite and infinite are not different, since you did not define the finite in order to define correctly the infinite
And may be the AP can teach you a better lesson in this regard
But, still you would not get anything out of this free lecture for sure
And it does not any matter
And the real difference of sqrt(2) and its decimal rational expansion is really unreal number, because your infinity is defined as unreal number
Regards
Bassam King Karzeddin
15th, April, 2017
And the stupids would never realize that when they assume their limits exist at their fake Paradise (called infinity) for their integer (n) tending to infinity (which is not real by definition), then its reciprocal (1/n) is equivalent to something as (1/unreal) which is unreal too, for sure

But the lovers of legendary stories makes it deliberately as real as zero (by their own damn definition), just to justify their fake results (that is all)

and this is how they got used and addicted to it since it can sh*t endless results and theorems more than any heavy rains for sure

BK
b***@gmail.com
2017-04-29 14:08:38 UTC
Raw Message
They are not called unreal numbers. They are called Unicorn
numbers. There are female and male Unicorn numbers.

The complex Unicorn numbers have an asian part and an
european part. Here have a Unicorn cushion:

unicorn cushion
Post by bassam king karzeddin
And the stupids would never realize that when they assume their limits exist at their fake Paradise (called infinity) for their integer (n) tending to infinity (which is not real by definition), then its reciprocal (1/n) is equivalent to something as (1/unreal) which is unreal too, for sure
But the lovers of legendary stories makes it deliberately as real as zero (by their own damn definition), just to justify their fake results (that is all)
and this is how they got used and addicted to it since it can sh*t endless results and theorems more than any heavy rains for sure
BK
b***@gmail.com
2017-05-02 19:56:20 UTC
Raw Message
And did you burn your own book BKK, since it uses
infinity? Ever heard of methods developing series
of implicit functions?

Here have a look:

Taylor Polynomials of Implicit Functions,
of Inverse Functions, and of Solutions of
Ordinary Differential Equations
WOLFRAM KOEPF - 1994
http://www.mathematik.uni-kassel.de/~koepf/Publikationen/Koepf1994.pdf

Only 10 pages
Anyway, all their works was simply from my general
formula provided in my book (1994), titled
Solution of equations by power series (67 pages only)
b***@gmail.com
2017-05-02 19:59:43 UTC
Raw Message
For the Bring radical try the implicit function by:

y^5-y+x = 0

I didn't try yet, dunno how difficult it will be to
read off the systematic in the coefficients.

Possibly there might be some CAS around which could
also could give that as an output.
Post by b***@gmail.com
And did you burn your own book BKK, since it uses
infinity? Ever heard of methods developing series
of implicit functions?
Taylor Polynomials of Implicit Functions,
of Inverse Functions, and of Solutions of
Ordinary Differential Equations
WOLFRAM KOEPF - 1994
http://www.mathematik.uni-kassel.de/~koepf/Publikationen/Koepf1994.pdf
Only 10 pages
Anyway, all their works was simply from my general
formula provided in my book (1994), titled
Solution of equations by power series (67 pages only)
b***@gmail.com
2017-05-03 20:55:55 UTC
Raw Message
For trinomials BKK is probably too late:

Series for all the Roots of a Trinomial Equation
The American Mathematical Monthly - Albert Eagle
Vol. 46, No. 7 (Aug. - Sep., 1939), pp. 422-425

https://www.jstor.org/stable/2303036
Anyway, all their works was simply from my general
formula provided in my book (1994), titled
Solution of equations by power series (67 pages only)
e***@arcor.de
2017-05-04 03:50:50 UTC
Raw Message
Post by bassam king karzeddin
Created by St. Georg? Maybe, the confusion goes back at least to a Bernoulli and to Leibniz who declared the continuum a labyrinth instead of defining it as something every part of which has parts while a point is something that has no parts. Peirce was certainly not drunk when he spoke of mere potentialities.

Leibniz' relative infinity logically negates the property of being endless.
To some extent, the mathematical paradise is based on pragmatic split thinking. WM deserves appreciation for his effort to criticize some consequences.

I also appreciate Katz. I would even more appreciate someone who seriously dealt with McEachern because QM comes with a bundle of futile oddities, too.
WM
2017-04-15 16:16:39 UTC
Raw Message
Post by b***@gmail.com
Well D = 1.41421356237... is a limes its the same as your arithmo-
1
1 2
1 2 3
1 2 3 4
...
No. The limit does exist whereas I show that the figure cannot exist.

Regards, WM
bassam king karzeddin
2017-04-17 16:10:39 UTC
Raw Message
Post by b***@gmail.com
So sqrt(2) = 1.41421356237... + e, where e is an infinitessimal e <> 0,
and where we have e^2 = 0, i.e. it is nilsquare.
An Invitation to Smooth Infinitesimal Analysis John L. Bell
http://publish.uwo.ca/~jbell/invitation%20to%20SIA.pdf
Or what property does your difference between sqrt(2) and 1.41421356237...
have? There must be a difference when sqrt(2) <> 1.41421356237...
e = sqrt(2) - 1.41421356237...
e <> 0
What property does your infinitessimal e have? Is it nilsquare?
Or does it have some other property?
Post by bassam king karzeddin
Actually this only concept in mathematics needs few minutes to verify its legality of being considered as any real good and useful concept or just a mere big fallacy that is more than meaningless and a kind of madness, wonder!
It is also stranger how it led the mathematicians to built on it so many huge volumes of baseless mathematics that is good enough for little carpentry works
And even much stranger that they had generated so many types of more infinities to the science of mathematics.
But the oddest thing is that mainstream common mathematicians never realize that such concepts are so meaningless the same way their results that they obtain relying on that fake concept
And naturally such concept is indeed a real paradise for any jugglers to create so many meaningless games and shamelessly consider it as a real science
But the fact that any theorem or formula or result that is associated with such silly concept as infinity, is also so silly but may be good for entertainment
Since mainly, no definite rules with it, nor any real existence (being unreal: by its own definition)
So, this flowed concept would make it very easy in the near future to make mathematics get doubled and tripled and even grows indefinitely in the fake unreal direction to its collapsed limits, for sure
However, many refutations of such meaningless concept was provided in my posts, beside many others
Regards
Bassam King Karzeddin
15 th, April, 2017
brusegan would never learn anything so marvelous and new deliberately, wasting other people's time and insists to be so stubborn as always as usual, despite being informed more than anyone else personally about the irrefutable and published proofs based on INTEGER analysis and not simply that meaningless real (I mean unreal or complex fectious analysis)

So, should I copy and paste the proof again and again with remarkable note that no one could invalidate them too, for sure

So, what does the mathematics mean exactly by: sqrt(2) = 1.41421356237...

The mathematics is simply are in search of the greatest rational number that is less than sqrt(2), which obviously does not exist, (so, this is the whole silly story), but sqrt(2) itself exists independently from any rational illegal representation despite many deniers)

And it is also created from the unity (one), that created and measured the rationals too

sqrt(2) is simply belonging to the first layer of rational numbers, where the rational numbers are the natural original layer of real numbers, it is simply the measure of two, (but under the first square root operation), where every non negative rational must have unique square root, and unique double square root, and generally many multi square roots as defined and was proved in my new theorems about the real numbers,

So, there is still unreal difference (e = sqrt(2) - 1.41421356237...), where the infinite decimal of sqrt(2) is also unreal numbers

And nothing indeed of real original existence can be expressed also as a combination of two unreal and non existing terms, since simply the later term is simply associated with unreal and non existing term called (INFINITY)

In short, one by definition is the only creator of real existing numbers, whereas all other (associated with any kind of infinity) numbers are Ghost numbers, and non existing numbers for sure

Regards
Bassam King Karzeddin
17 th, April, 2017
bassam king karzeddin
2017-04-17 16:13:19 UTC
Raw Message
Post by bassam king karzeddin
Post by b***@gmail.com
So sqrt(2) = 1.41421356237... + e, where e is an infinitessimal e <> 0,
and where we have e^2 = 0, i.e. it is nilsquare.
An Invitation to Smooth Infinitesimal Analysis John L. Bell
http://publish.uwo.ca/~jbell/invitation%20to%20SIA.pdf
Or what property does your difference between sqrt(2) and 1.41421356237...
have? There must be a difference when sqrt(2) <> 1.41421356237...
e = sqrt(2) - 1.41421356237...
e <> 0
What property does your infinitessimal e have? Is it nilsquare?
Or does it have some other property?
Post by bassam king karzeddin
Actually this only concept in mathematics needs few minutes to verify its legality of being considered as any real good and useful concept or just a mere big fallacy that is more than meaningless and a kind of madness, wonder!
It is also stranger how it led the mathematicians to built on it so many huge volumes of baseless mathematics that is good enough for little carpentry works
And even much stranger that they had generated so many types of more infinities to the science of mathematics.
But the oddest thing is that mainstream common mathematicians never realize that such concepts are so meaningless the same way their results that they obtain relying on that fake concept
And naturally such concept is indeed a real paradise for any jugglers to create so many meaningless games and shamelessly consider it as a real science
But the fact that any theorem or formula or result that is associated with such silly concept as infinity, is also so silly but may be good for entertainment
Since mainly, no definite rules with it, nor any real existence (being unreal: by its own definition)
So, this flowed concept would make it very easy in the near future to make mathematics get doubled and tripled and even grows indefinitely in the fake unreal direction to its collapsed limits, for sure
However, many refutations of such meaningless concept was provided in my posts, beside many others
Regards
Bassam King Karzeddin
15 th, April, 2017
brusegan would never learn anything so marvelous and new deliberately, wasting other people's time and insists to be so stubborn as always as usual, despite being informed more than anyone else personally about the irrefutable and published proofs based on INTEGER analysis and not simply that meaningless real (I mean unreal or complex fectious analysis)
So, should I copy and paste the proof again and again with remarkable note that no one could invalidate them too, for sure
So, what does the mathematics mean exactly by: sqrt(2) = 1.41421356237...
The mathematics is simply are in search of the greatest rational number that is less than sqrt(2), which obviously does not exist, (so, this is the whole silly story), but sqrt(2) itself exists independently from any rational illegal representation despite many deniers)
And it is also created from the unity (one), that created and measured the rationals too
sqrt(2) is simply belonging to the first layer of rational numbers, where the rational numbers are the natural original layer of real numbers, it is simply the measure of two, (but under the first square root operation), where every non negative rational must have unique square root, and unique double square root, and generally many multi square roots as defined and was proved in my new theorems about the real numbers,
So, there is still unreal difference (e = sqrt(2) - 1.41421356237...), where the infinite decimal of sqrt(2) is also unreal numbers
And nothing indeed of real original existence can be expressed also as a combination of two unreal and non existing terms, since simply the later term is simply associated with unreal and non existing term called (INFINITY)
In short, one by definition is the only creator of real existing numbers, whereas all other (associated with any kind of infinity) numbers are Ghost numbers, and non existing numbers for sure
Regards
Bassam King Karzeddin
17 th, April, 2017
b***@gmail.com
2017-04-17 19:16:14 UTC
Raw Message
Well its indeed the case that the infinity border has finally
been found. An attempt was made by AP and he found 10^603.

But he made an error, he was looking for 000 in the 10-base
representation of pi. But we need to look for 888 in the

16-base representation of pi. The infinity border is then
only 4'294'967'296, and we can conclude that infinity is a

quite harmless and tiny concept, beyond the holy grail. But
the credit goes to me, already published on arvix, and not AP.
Post by bassam king karzeddin
Post by b***@gmail.com
So sqrt(2) = 1.41421356237... + e, where e is an infinitessimal e <> 0,
and where we have e^2 = 0, i.e. it is nilsquare.
An Invitation to Smooth Infinitesimal Analysis John L. Bell
http://publish.uwo.ca/~jbell/invitation%20to%20SIA.pdf
Or what property does your difference between sqrt(2) and 1.41421356237...
have? There must be a difference when sqrt(2) <> 1.41421356237...
e = sqrt(2) - 1.41421356237...
e <> 0
What property does your infinitessimal e have? Is it nilsquare?
Or does it have some other property?
Post by bassam king karzeddin
Actually this only concept in mathematics needs few minutes to verify its legality of being considered as any real good and useful concept or just a mere big fallacy that is more than meaningless and a kind of madness, wonder!
It is also stranger how it led the mathematicians to built on it so many huge volumes of baseless mathematics that is good enough for little carpentry works
And even much stranger that they had generated so many types of more infinities to the science of mathematics.
But the oddest thing is that mainstream common mathematicians never realize that such concepts are so meaningless the same way their results that they obtain relying on that fake concept
And naturally such concept is indeed a real paradise for any jugglers to create so many meaningless games and shamelessly consider it as a real science
But the fact that any theorem or formula or result that is associated with such silly concept as infinity, is also so silly but may be good for entertainment
Since mainly, no definite rules with it, nor any real existence (being unreal: by its own definition)
So, this flowed concept would make it very easy in the near future to make mathematics get doubled and tripled and even grows indefinitely in the fake unreal direction to its collapsed limits, for sure
However, many refutations of such meaningless concept was provided in my posts, beside many others
Regards
Bassam King Karzeddin
15 th, April, 2017
brusegan would never learn anything so marvelous and new deliberately, wasting other people's time and insists to be so stubborn as always as usual, despite being informed more than anyone else personally about the irrefutable and published proofs based on INTEGER analysis and not simply that meaningless real (I mean unreal or complex fectious analysis)
So, should I copy and paste the proof again and again with remarkable note that no one could invalidate them too, for sure
So, what does the mathematics mean exactly by: sqrt(2) = 1.41421356237...
The mathematics is simply are in search of the greatest rational number that is less than sqrt(2), which obviously does not exist, (so, this is the whole silly story), but sqrt(2) itself exists independently from any rational illegal representation despite many deniers)
And it is also created from the unity (one), that created and measured the rationals too
sqrt(2) is simply belonging to the first layer of rational numbers, where the rational numbers are the natural original layer of real numbers, it is simply the measure of two, (but under the first square root operation), where every non negative rational must have unique square root, and unique double square root, and generally many multi square roots as defined and was proved in my new theorems about the real numbers,
So, there is still unreal difference (e = sqrt(2) - 1.41421356237...), where the infinite decimal of sqrt(2) is also unreal numbers
And nothing indeed of real original existence can be expressed also as a combination of two unreal and non existing terms, since simply the later term is simply associated with unreal and non existing term called (INFINITY)
In short, one by definition is the only creator of real existing numbers, whereas all other (associated with any kind of infinity) numbers are Ghost numbers, and non existing numbers for sure
Regards
Bassam King Karzeddin
17 th, April, 2017
2017-04-15 20:06:53 UTC
Raw Message
Post by bassam king karzeddin
Actually this only concept in mathematics needs few minutes to verify its legality of being considered as any real good and useful concept or just a mere big fallacy that is more than meaningless and a kind of madness, wonder!
It is also stranger how it led the mathematicians to built on it so many huge volumes of baseless mathematics that is good enough for little carpentry works
And even much stranger that they had generated so many types of more infinities to the science of mathematics.
But the oddest thing is that mainstream common mathematicians never realize that such concepts are so meaningless the same way their results that they obtain relying on that fake concept
And naturally such concept is indeed a real paradise for any jugglers to create so many meaningless games and shamelessly consider it as a real science
But the fact that any theorem or formula or result that is associated with such silly concept as infinity, is also so silly but may be good for entertainment
Since mainly, no definite rules with it, nor any real existence (being unreal: by its own definition)
So, this flowed concept would make it very easy in the near future to make mathematics get doubled and tripled and even grows indefinitely in the fake unreal direction to its collapsed limits, for sure
However, many refutations of such meaningless concept was provided in my posts, beside many others
Regards
Bassam King Karzeddin
15 th, April, 2017
The only odd thing is that you cannot see how wrong you are.
Barstool Kim Kardashian
2017-04-15 23:02:06 UTC
Raw Message
Shut the fuck up mathforum.org imbecile.
bassam king karzeddin
2017-04-16 06:02:33 UTC
Raw Message
Post by Barstool Kim Kardashian
Shut the fuck up mathforum.org imbecile.
Imbecile No. 18, I think, identified immediately from his first and hopefully the last post

And guess what kind of maths those idiots can teach you?

And guess what kind of force that makes them register just to say a half a line of nonsense?

BK
Dan Christensen
2017-04-16 15:56:25 UTC
Raw Message
Post by bassam king karzeddin
Actually this only concept in mathematics needs few minutes to verify its legality of being considered as any real good and useful concept or just a mere big fallacy that is more than meaningless and a kind of madness, wonder!
I know that you and your fellow cranks are not overly concerned about actually developing mathematics from your nutty ideas, but just try to formally develop even basic arithmetic (e.g. proving that addition on N is associative and commutative) without an infinite supply of numbers. I think you will find it impossible.

Dan

Visit my Math Blog at http://www.dcproof.wordpress.com
Ross A. Finlayson
2017-04-18 01:12:48 UTC
Raw Message
Post by bassam king karzeddin
Actually this only concept in mathematics needs few minutes to verify its legality of being considered as any real good and useful concept or just a mere big fallacy that is more than meaningless and a kind of madness, wonder!
It is also stranger how it led the mathematicians to built on it so many huge volumes of baseless mathematics that is good enough for little carpentry works
And even much stranger that they had generated so many types of more infinities to the science of mathematics.
But the oddest thing is that mainstream common mathematicians never realize that such concepts are so meaningless the same way their results that they obtain relying on that fake concept
And naturally such concept is indeed a real paradise for any jugglers to create so many meaningless games and shamelessly consider it as a real science
But the fact that any theorem or formula or result that is associated with such silly concept as infinity, is also so silly but may be good for entertainment
Since mainly, no definite rules with it, nor any real existence (being unreal: by its own definition)
So, this flowed concept would make it very easy in the near future to make mathematics get doubled and tripled and even grows indefinitely in the fake unreal direction to its collapsed limits, for sure
However, many refutations of such meaningless concept was provided in my posts, beside many others
Regards
Bassam King Karzeddin
15 th, April, 2017
Infinity is the purview of some of our greatest
thinkers, apparently not retro-finitist crankety-
troll spam-puppets and their similar (or is that,

Infinity is bigger.

The universe is infinite / infinite sets are equivalent
(and yes I'm rather familiar with the modernly standard).

Infinity (and simply more than finitely many) finds itself
central and fundamental in the mathematics.

Anything less is rather mute on the matter.

Begone foul troll-bots.
bassam king karzeddin
2017-04-18 12:39:19 UTC
Raw Message
Post by Ross A. Finlayson
Post by bassam king karzeddin
Actually this only concept in mathematics needs few minutes to verify its legality of being considered as any real good and useful concept or just a mere big fallacy that is more than meaningless and a kind of madness, wonder!
It is also stranger how it led the mathematicians to built on it so many huge volumes of baseless mathematics that is good enough for little carpentry works
And even much stranger that they had generated so many types of more infinities to the science of mathematics.
But the oddest thing is that mainstream common mathematicians never realize that such concepts are so meaningless the same way their results that they obtain relying on that fake concept
And naturally such concept is indeed a real paradise for any jugglers to create so many meaningless games and shamelessly consider it as a real science
But the fact that any theorem or formula or result that is associated with such silly concept as infinity, is also so silly but may be good for entertainment
Since mainly, no definite rules with it, nor any real existence (being unreal: by its own definition)
So, this flowed concept would make it very easy in the near future to make mathematics get doubled and tripled and even grows indefinitely in the fake unreal direction to its collapsed limits, for sure
However, many refutations of such meaningless concept was provided in my posts, beside many others
Regards
Bassam King Karzeddin
15 th, April, 2017
Infinity is the purview of some of our greatest
thinkers,
But I had proved (in my old and recent posts) and beyond any little doubt that those majority of alleged great thinkers were actually skilled carpenters and not absolutely any true mathematicians for sure

[snip the garbage]
Post by Ross A. Finlayson
Infinity is bigger.
Of course infinity is bigger than any number most likely you mean, especially that infinity is not even any real number (by its definition), wonder!

Especially that had been stated and settled by your great thinkers, wonder!

Infinity is also longer than any tree on earth, heavier than any mountain since it is not a number nor anything else, wonder!
Post by Ross A. Finlayson
The universe is infinite / infinite sets are equivalent
(and yes I'm rather familiar with the modernly standard).
Yes of course, infinity is the magical tool to understand the whole universe too, especially that it is not any real nor any number, so wonderful infinity indeed, is not it? wonder!

And that is why they say universe is expanding, because universe is infinite, is not it? wonder!
Post by Ross A. Finlayson
Infinity (and simply more than finitely many) finds itself
central and fundamental in the mathematics.
It is not only central, but also so wonderful Paradise, that gives the greatest chances for so many skilled carpenters to oddly become as greatest thinkers for sure!

But only we have to believe in it, to be reworded in that Paradise, otherwise hell is our final destiny, and naturally all the deniers of infinity must be punished to death also, why not?

But for all true believers of infinities, glory and fame is awaiting you since there are still billions of undiscovered formulas for (pi), for (e), for zeta(x), ...etc, motivate your self on its endless use where you can create new mathematics that can fill the whole universe, leaving those ultra finite mentally retarded cornered and out of date

And once they ask you why one and zero become alike at that Paradise called infinity, you tell them it is only one of the endless grace of infinity, at infinity all numbers are alike and equals, at infinity there is absolute justice where no real number is simply greater or less than any other number

Yes, this is the absolute democracy at our Promised Paradise but only if we follow its instruction,
Post by Ross A. Finlayson
Anything less is rather mute on the matter.
Of course, nothing can be greater than our infinity and nothing can be less than our negative infinity, and once you make it upside down, nothing would come out of it for sure
Post by Ross A. Finlayson
Begone foul troll-bots.
And the Trolls are merely Trolls (Same inhabitants of old centuries) for sure

So, Happy infinity and many returns of many other infinities, enjoy it forever

Indeed, incurable disease infinity is, psychologist help is urgently required to help and cure those helpless little mind birds living alone in that fake Paradise

With all sorrow and sincere wishes that many sick people get completely healed of infinity and recover soon

Bassam King Karzeddin
18 th, April, 2017
b***@gmail.com
2017-04-18 13:01:30 UTC
Raw Message
Actually AP made the following error in his computation. Since
Egyptians already used hexdecimal system, it is important to use
a 16-base system when looking at pi, and not a 10-base system.

Further the critical tripple is not 000, but 888, since 8 is half of
16, and it is quite obvious that the tractrix will stumble upon such
an occurence so that we get

the infinity border is 16^8 and not 10^603.

Here are the first 831 hex digits of pi:

3.243f6a8885a308d313198a2e03707344a4093822299f31d0082efa98ec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Post by bassam king karzeddin
Post by Ross A. Finlayson
Post by bassam king karzeddin
Actually this only concept in mathematics needs few minutes to verify its legality of being considered as any real good and useful concept or just a mere big fallacy that is more than meaningless and a kind of madness, wonder!
It is also stranger how it led the mathematicians to built on it so many huge volumes of baseless mathematics that is good enough for little carpentry works
And even much stranger that they had generated so many types of more infinities to the science of mathematics.
But the oddest thing is that mainstream common mathematicians never realize that such concepts are so meaningless the same way their results that they obtain relying on that fake concept
And naturally such concept is indeed a real paradise for any jugglers to create so many meaningless games and shamelessly consider it as a real science
But the fact that any theorem or formula or result that is associated with such silly concept as infinity, is also so silly but may be good for entertainment
Since mainly, no definite rules with it, nor any real existence (being unreal: by its own definition)
So, this flowed concept would make it very easy in the near future to make mathematics get doubled and tripled and even grows indefinitely in the fake unreal direction to its collapsed limits, for sure
However, many refutations of such meaningless concept was provided in my posts, beside many others
Regards
Bassam King Karzeddin
15 th, April, 2017
Infinity is the purview of some of our greatest
thinkers,
But I had proved (in my old and recent posts) and beyond any little doubt that those majority of alleged great thinkers were actually skilled carpenters and not absolutely any true mathematicians for sure
[snip the garbage]
Post by Ross A. Finlayson
Infinity is bigger.
Of course infinity is bigger than any number most likely you mean, especially that infinity is not even any real number (by its definition), wonder!
Especially that had been stated and settled by your great thinkers, wonder!
Infinity is also longer than any tree on earth, heavier than any mountain since it is not a number nor anything else, wonder!
Post by Ross A. Finlayson
The universe is infinite / infinite sets are equivalent
(and yes I'm rather familiar with the modernly standard).
Yes of course, infinity is the magical tool to understand the whole universe too, especially that it is not any real nor any number, so wonderful infinity indeed, is not it? wonder!
And that is why they say universe is expanding, because universe is infinite, is not it? wonder!
Post by Ross A. Finlayson
Infinity (and simply more than finitely many) finds itself
central and fundamental in the mathematics.
It is not only central, but also so wonderful Paradise, that gives the greatest chances for so many skilled carpenters to oddly become as greatest thinkers for sure!
But only we have to believe in it, to be reworded in that Paradise, otherwise hell is our final destiny, and naturally all the deniers of infinity must be punished to death also, why not?
But for all true believers of infinities, glory and fame is awaiting you since there are still billions of undiscovered formulas for (pi), for (e), for zeta(x), ...etc, motivate your self on its endless use where you can create new mathematics that can fill the whole universe, leaving those ultra finite mentally retarded cornered and out of date
And once they ask you why one and zero become alike at that Paradise called infinity, you tell them it is only one of the endless grace of infinity, at infinity all numbers are alike and equals, at infinity there is absolute justice where no real number is simply greater or less than any other number
Yes, this is the absolute democracy at our Promised Paradise but only if we follow its instruction,
Post by Ross A. Finlayson
Anything less is rather mute on the matter.
Of course, nothing can be greater than our infinity and nothing can be less than our negative infinity, and once you make it upside down, nothing would come out of it for sure
Post by Ross A. Finlayson
Begone foul troll-bots.
And the Trolls are merely Trolls (Same inhabitants of old centuries) for sure
So, Happy infinity and many returns of many other infinities, enjoy it forever
Indeed, incurable disease infinity is, psychologist help is urgently required to help and cure those helpless little mind birds living alone in that fake Paradise
With all sorrow and sincere wishes that many sick people get completely healed of infinity and recover soon
Bassam King Karzeddin
18 th, April, 2017
bassam king karzeddin
2017-07-30 11:48:58 UTC
Raw Message
Post by bassam king karzeddin
Actually this only concept in mathematics needs few minutes to verify its legality of being considered as any real good and useful concept or just a mere big fallacy that is more than meaningless and a kind of madness, wonder!
It is also stranger how it led the mathematicians to built on it so many huge volumes of baseless mathematics that is good enough for little carpentry works
And even much stranger that they had generated so many types of more infinities to the science of mathematics.
But the oddest thing is that mainstream common mathematicians never realize that such concepts are so meaningless the same way their results that they obtain relying on that fake concept
And naturally such concept is indeed a real paradise for any jugglers to create so many meaningless games and shamelessly consider it as a real science
But the fact that any theorem or formula or result that is associated with such silly concept as infinity, is also so silly but may be good for entertainment
Since mainly, no definite rules with it, nor any real existence (being unreal: by its own definition)
So, this flowed concept would make it very easy in the near future to make mathematics get doubled and tripled and even grows indefinitely in the fake unreal direction to its collapsed limits, for sure
However, many refutations of such meaningless concept was provided in my posts, beside many others
Regards
Bassam King Karzeddin
15 th, April, 2017
And if Infinity was defined being an unreal number, then why the hell you apply the well known mathematical operations on it? wonder about this absolute stupidity by the top professional mathematicians for sure

But the reasons are so obvious, if not applying those known operations then how come they can legalize new discoveries? wonder

Ok, let us illustrate it for kids in order to understand the huge fallacy in that known mind of a mathematician

Let us say a Donkey isn't a number, then can you (Genius) legalize those mathematical operations as (adding, subtracting, multiplying, divideing, or operating square root operations) on that Donkey? wonder

Of course, only a Genious mathematician can deal with that Donkey, especially that would give him so many rewards for sure

Otherwise, what is the use of mathematics then? wonder!

But be very happy Genious mathematicians, there are certainly many golden chances to make many famous results from that trick alleged term called (Infinity), for instance, they made sum of all integers as (-1/12) and much more nonsenses mathematics than this, with many videos where the poor sheep got so fascinated beyond limits, they simply love any fiction as long as it appears consistent in their silo standards

And indeed Infinity concept would give a chance for almost anyone who plays carefully with it to be considered as a GENIOUS MATHEMATICIANS for sure

But, very, unfortunately (Infinity doesn't exist) for sure

So, get back to your original state of Donkey numbers Genious mathematicians

BKK
Dan Christensen
2017-07-30 12:13:01 UTC
Raw Message
Post by bassam king karzeddin
Post by bassam king karzeddin
Actually this only concept in mathematics needs few minutes to verify its legality of being considered as any real good and useful concept or just a mere big fallacy that is more than meaningless and a kind of madness, wonder!
It is also stranger how it led the mathematicians to built on it so many huge volumes of baseless mathematics that is good enough for little carpentry works
And even much stranger that they had generated so many types of more infinities to the science of mathematics.
But the oddest thing is that mainstream common mathematicians never realize that such concepts are so meaningless the same way their results that they obtain relying on that fake concept
And naturally such concept is indeed a real paradise for any jugglers to create so many meaningless games and shamelessly consider it as a real science
But the fact that any theorem or formula or result that is associated with such silly concept as infinity, is also so silly but may be good for entertainment
Since mainly, no definite rules with it, nor any real existence (being unreal: by its own definition)
So, this flowed concept would make it very easy in the near future to make mathematics get doubled and tripled and even grows indefinitely in the fake unreal direction to its collapsed limits, for sure
However, many refutations of such meaningless concept was provided in my posts, beside many others
Regards
Bassam King Karzeddin
15 th, April, 2017
And if Infinity was defined being an unreal number, then why the hell you apply the well known mathematical operations on it? wonder about this absolute stupidity by the top professional mathematicians for sure
I see you have STILL been unable to formally develop even basic arithmetic (e.g. proving that addition on N is associative and commutative) in your goofy system, BKK. Talk about absolute stupidity! It really is back to the drawing board for you... for sure. (Hee, hee!)

Dan
Markus Klyver
2017-08-01 15:21:32 UTC
Raw Message
Post by bassam king karzeddin
Post by bassam king karzeddin
Actually this only concept in mathematics needs few minutes to verify its legality of being considered as any real good and useful concept or just a mere big fallacy that is more than meaningless and a kind of madness, wonder!
It is also stranger how it led the mathematicians to built on it so many huge volumes of baseless mathematics that is good enough for little carpentry works
And even much stranger that they had generated so many types of more infinities to the science of mathematics.
But the oddest thing is that mainstream common mathematicians never realize that such concepts are so meaningless the same way their results that they obtain relying on that fake concept
And naturally such concept is indeed a real paradise for any jugglers to create so many meaningless games and shamelessly consider it as a real science
But the fact that any theorem or formula or result that is associated with such silly concept as infinity, is also so silly but may be good for entertainment
Since mainly, no definite rules with it, nor any real existence (being unreal: by its own definition)
So, this flowed concept would make it very easy in the near future to make mathematics get doubled and tripled and even grows indefinitely in the fake unreal direction to its collapsed limits, for sure
However, many refutations of such meaningless concept was provided in my posts, beside many others
Regards
Bassam King Karzeddin
15 th, April, 2017
And if Infinity was defined being an unreal number, then why the hell you apply the well known mathematical operations on it? wonder about this absolute stupidity by the top professional mathematicians for sure
But the reasons are so obvious, if not applying those known operations then how come they can legalize new discoveries? wonder
Ok, let us illustrate it for kids in order to understand the huge fallacy in that known mind of a mathematician
Let us say a Donkey isn't a number, then can you (Genius) legalize those mathematical operations as (adding, subtracting, multiplying, divideing, or operating square root operations) on that Donkey? wonder
Of course, only a Genious mathematician can deal with that Donkey, especially that would give him so many rewards for sure
Otherwise, what is the use of mathematics then? wonder!
But be very happy Genious mathematicians, there are certainly many golden chances to make many famous results from that trick alleged term called (Infinity), for instance, they made sum of all integers as (-1/12) and much more nonsenses mathematics than this, with many videos where the poor sheep got so fascinated beyond limits, they simply love any fiction as long as it appears consistent in their silo standards
And indeed Infinity concept would give a chance for almost anyone who plays carefully with it to be considered as a GENIOUS MATHEMATICIANS for sure
But, very, unfortunately (Infinity doesn't exist) for sure
So, get back to your original state of Donkey numbers Genious mathematicians
BKK
We can extend our mathematical operations for real numbers to be defined for infinity as well. You can define addition for donkeys as well, if you want to.
bassam king karzeddin
2017-08-02 15:17:52 UTC
Raw Message
Post by Markus Klyver
Post by bassam king karzeddin
Post by bassam king karzeddin
Actually this only concept in mathematics needs few minutes to verify its legality of being considered as any real good and useful concept or just a mere big fallacy that is more than meaningless and a kind of madness, wonder!
It is also stranger how it led the mathematicians to built on it so many huge volumes of baseless mathematics that is good enough for little carpentry works
And even much stranger that they had generated so many types of more infinities to the science of mathematics.
But the oddest thing is that mainstream common mathematicians never realize that such concepts are so meaningless the same way their results that they obtain relying on that fake concept
And naturally such concept is indeed a real paradise for any jugglers to create so many meaningless games and shamelessly consider it as a real science
But the fact that any theorem or formula or result that is associated with such silly concept as infinity, is also so silly but may be good for entertainment
Since mainly, no definite rules with it, nor any real existence (being unreal: by its own definition)
So, this flowed concept would make it very easy in the near future to make mathematics get doubled and tripled and even grows indefinitely in the fake unreal direction to its collapsed limits, for sure
However, many refutations of such meaningless concept was provided in my posts, beside many others
Regards
Bassam King Karzeddin
15 th, April, 2017
And if Infinity was defined being an unreal number, then why the hell you apply the well known mathematical operations on it? wonder about this absolute stupidity by the top professional mathematicians for sure
But the reasons are so obvious, if not applying those known operations then how come they can legalize new discoveries? wonder
Ok, let us illustrate it for kids in order to understand the huge fallacy in that known mind of a mathematician
Let us say a Donkey isn't a number, then can you (Genius) legalize those mathematical operations as (adding, subtracting, multiplying, divideing, or operating square root operations) on that Donkey? wonder
Of course, only a Genious mathematician can deal with that Donkey, especially that would give him so many rewards for sure
Otherwise, what is the use of mathematics then? wonder!
But be very happy Genious mathematicians, there are certainly many golden chances to make many famous results from that trick alleged term called (Infinity), for instance, they made sum of all integers as (-1/12) and much more nonsenses mathematics than this, with many videos where the poor sheep got so fascinated beyond limits, they simply love any fiction as long as it appears consistent in their silo standards
And indeed Infinity concept would give a chance for almost anyone who plays carefully with it to be considered as a GENIOUS MATHEMATICIANS for sure
But, very, unfortunately (Infinity doesn't exist) for sure
So, get back to your original state of Donkey numbers Genious mathematicians
BKK
We can extend our mathematical operations for real numbers to be defined for infinity as well. You can define addition for donkeys as well, if you want to.
Go a head and extend the mathematical operations for infinity and donkeys, there may be a great chance that donkey like monkey might produce many theorems as well, especially if playing so carefully with the term infinity in mathematics, for sure
BKK
Markus Klyver
2017-08-02 21:56:54 UTC
Raw Message
Post by bassam king karzeddin
Post by Markus Klyver
Post by bassam king karzeddin
Post by bassam king karzeddin
Actually this only concept in mathematics needs few minutes to verify its legality of being considered as any real good and useful concept or just a mere big fallacy that is more than meaningless and a kind of madness, wonder!
It is also stranger how it led the mathematicians to built on it so many huge volumes of baseless mathematics that is good enough for little carpentry works
And even much stranger that they had generated so many types of more infinities to the science of mathematics.
But the oddest thing is that mainstream common mathematicians never realize that such concepts are so meaningless the same way their results that they obtain relying on that fake concept
And naturally such concept is indeed a real paradise for any jugglers to create so many meaningless games and shamelessly consider it as a real science
But the fact that any theorem or formula or result that is associated with such silly concept as infinity, is also so silly but may be good for entertainment
Since mainly, no definite rules with it, nor any real existence (being unreal: by its own definition)
So, this flowed concept would make it very easy in the near future to make mathematics get doubled and tripled and even grows indefinitely in the fake unreal direction to its collapsed limits, for sure
However, many refutations of such meaningless concept was provided in my posts, beside many others
Regards
Bassam King Karzeddin
15 th, April, 2017
And if Infinity was defined being an unreal number, then why the hell you apply the well known mathematical operations on it? wonder about this absolute stupidity by the top professional mathematicians for sure
But the reasons are so obvious, if not applying those known operations then how come they can legalize new discoveries? wonder
Ok, let us illustrate it for kids in order to understand the huge fallacy in that known mind of a mathematician
Let us say a Donkey isn't a number, then can you (Genius) legalize those mathematical operations as (adding, subtracting, multiplying, divideing, or operating square root operations) on that Donkey? wonder
Of course, only a Genious mathematician can deal with that Donkey, especially that would give him so many rewards for sure
Otherwise, what is the use of mathematics then? wonder!
But be very happy Genious mathematicians, there are certainly many golden chances to make many famous results from that trick alleged term called (Infinity), for instance, they made sum of all integers as (-1/12) and much more nonsenses mathematics than this, with many videos where the poor sheep got so fascinated beyond limits, they simply love any fiction as long as it appears consistent in their silo standards
And indeed Infinity concept would give a chance for almost anyone who plays carefully with it to be considered as a GENIOUS MATHEMATICIANS for sure
But, very, unfortunately (Infinity doesn't exist) for sure
So, get back to your original state of Donkey numbers Genious mathematicians
BKK
We can extend our mathematical operations for real numbers to be defined for infinity as well. You can define addition for donkeys as well, if you want to.
Go a head and extend the mathematical operations for infinity and donkeys, there may be a great chance that donkey like monkey might produce many theorems as well, especially if playing so carefully with the term infinity in mathematics, for sure
BKK
Sure. I define a ⊕ d := 1 for any real number a and any donkey d. I also define d ⊕ a := 1, hence the operator is commutative.

bassam king karzeddin
2017-08-03 09:48:09 UTC
Raw Message
Post by Markus Klyver
Post by bassam king karzeddin
Post by Markus Klyver
Post by bassam king karzeddin
Post by bassam king karzeddin
Actually this only concept in mathematics needs few minutes to verify its legality of being considered as any real good and useful concept or just a mere big fallacy that is more than meaningless and a kind of madness, wonder!
It is also stranger how it led the mathematicians to built on it so many huge volumes of baseless mathematics that is good enough for little carpentry works
And even much stranger that they had generated so many types of more infinities to the science of mathematics.
But the oddest thing is that mainstream common mathematicians never realize that such concepts are so meaningless the same way their results that they obtain relying on that fake concept
And naturally such concept is indeed a real paradise for any jugglers to create so many meaningless games and shamelessly consider it as a real science
But the fact that any theorem or formula or result that is associated with such silly concept as infinity, is also so silly but may be good for entertainment
Since mainly, no definite rules with it, nor any real existence (being unreal: by its own definition)
So, this flowed concept would make it very easy in the near future to make mathematics get doubled and tripled and even grows indefinitely in the fake unreal direction to its collapsed limits, for sure
However, many refutations of such meaningless concept was provided in my posts, beside many others
Regards
Bassam King Karzeddin
15 th, April, 2017
And if Infinity was defined being an unreal number, then why the hell you apply the well known mathematical operations on it? wonder about this absolute stupidity by the top professional mathematicians for sure
But the reasons are so obvious, if not applying those known operations then how come they can legalize new discoveries? wonder
Ok, let us illustrate it for kids in order to understand the huge fallacy in that known mind of a mathematician
Let us say a Donkey isn't a number, then can you (Genius) legalize those mathematical operations as (adding, subtracting, multiplying, divideing, or operating square root operations) on that Donkey? wonder
Of course, only a Genious mathematician can deal with that Donkey, especially that would give him so many rewards for sure
Otherwise, what is the use of mathematics then? wonder!
But be very happy Genious mathematicians, there are certainly many golden chances to make many famous results from that trick alleged term called (Infinity), for instance, they made sum of all integers as (-1/12) and much more nonsenses mathematics than this, with many videos where the poor sheep got so fascinated beyond limits, they simply love any fiction as long as it appears consistent in their silo standards
And indeed Infinity concept would give a chance for almost anyone who plays carefully with it to be considered as a GENIOUS MATHEMATICIANS for sure
But, very, unfortunately (Infinity doesn't exist) for sure
So, get back to your original state of Donkey numbers Genious mathematicians
BKK
We can extend our mathematical operations for real numbers to be defined for infinity as well. You can define addition for donkeys as well, if you want to.
Go a head and extend the mathematical operations for infinity and donkeys, there may be a great chance that donkey like monkey might produce many theorems as well, especially if playing so carefully with the term infinity in mathematics, for sure
BKK
Sure. I define a ⊕ d := 1 for any real number a and any donkey d. I also define d ⊕ a := 1, hence the operator is commutative.
And who agrees with you on this peculiar definition? (Please exclude the donkey)
BKK
Peter Percival
2017-08-01 18:23:07 UTC
Raw Message
Isn't infinity (in mathematics) actually a flawed concept?
Which infinity is that?

A few years ago Zdislav V. Kovarik made a post listing a dozen or more
meaning of the word "infinity" as used in different branches of
mathematics. I'm hoping that he won't mind me reposting it:

There is a long list of "infinities (with no claim to exhaustiveness):
infinity of the one-point compactification of N,
infinity of the one-point compactification of R,
infinity of the two-point compactification of R,
infinity of the one-point compactification of C,
infinities of the projective extension of the plane,
infinity of Lebesgue-type integration theory,
infinities of the non-standard extension of R,
infinities of the theory of ordinal numbers,
infinities of the theory of cardinal numbers,
infinity adjoined to normed spaces, whose neighborhoods are
complements of relatively compact sets,
infinity adjoined to normed spaces, whose neighborhoods are
complements of bounded sets,
infinity around absolute G-delta non-compact metric spaces,
infinity in the theory of convex optimization,
etc.;

each of these has a clear definition and a set of well-defined rules
for handling it.

And the winner is...
the really, really real infinity imagined by inexperienced debaters of
foundations of mathematics; this one has the advantage that it need
not be defined ("it's just there, don't you see?") and the user can
switch from one set of rules to another, without warning, and without
worrying about consistency, for the purpose of scoring points in idle
and uneducated (at least on one side) debates.
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
Markus Klyver
2017-08-02 13:15:12 UTC
Raw Message
Post by Peter Percival
Isn't infinity (in mathematics) actually a flawed concept?
Which infinity is that?
A few years ago Zdislav V. Kovarik made a post listing a dozen or more
meaning of the word "infinity" as used in different branches of
infinity of the one-point compactification of N,
infinity of the one-point compactification of R,
infinity of the two-point compactification of R,
infinity of the one-point compactification of C,
infinities of the projective extension of the plane,
infinity of Lebesgue-type integration theory,
infinities of the non-standard extension of R,
infinities of the theory of ordinal numbers,
infinities of the theory of cardinal numbers,
infinity adjoined to normed spaces, whose neighborhoods are
complements of relatively compact sets,
infinity adjoined to normed spaces, whose neighborhoods are
complements of bounded sets,
infinity around absolute G-delta non-compact metric spaces,
infinity in the theory of convex optimization,
etc.;
each of these has a clear definition and a set of well-defined rules
for handling it.
And the winner is...
the really, really real infinity imagined by inexperienced debaters of
foundations of mathematics; this one has the advantage that it need
not be defined ("it's just there, don't you see?") and the user can
switch from one set of rules to another, without warning, and without
worrying about consistency, for the purpose of scoring points in idle
and uneducated (at least on one side) debates.
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
Yeah, that's the thing with cranks. They assume infinity is this automagical number we mathematicians throw in without knowing what it means. The truth is, infinity can mean many things. And when we introduce a mathematical object to represent something we intuitively can think of infinity, we are always very careful with out definitions so that we know exactly what we are talking about.
t***@gmail.com
2017-08-01 18:43:36 UTC
Raw Message
Not at all. Enderton explained it well. First of all there is a common misnomer that the axiom of infinity actually has explicit or implicit connection to infinity, either naive or informed.

If I wrote down the axiom of infinity for you, or wrote down all the axioms of ZFC and asked you to tell me which one implies infinity exists, you would be unable to.

Here's the facts. We are big with numbers in math. So it would be nice to know if it could be the case that one day someone will prove 1=0. The simplest method for formalizing numbers is with set theory.

Axioms are neither true nor false. But think on this:
(1) Most people when inspecting the formal versions of the axioms of ZFC would not be able to spot which one has anything to do with infinity and (2) if we have a bunch of things we are willing to call sets then there must be a set consisting exactly of those sets we started with.

Does this make sense to you: there are numbers, which are specific sets, then we would like to consider "THE TOTALITY of all numbers" also a set.
Dan Christensen
2017-08-01 19:46:07 UTC
Raw Message
Post by t***@gmail.com
Not at all. Enderton explained it well. First of all there is a common misnomer that the axiom of infinity actually has explicit or implicit connection to infinity, either naive or informed.
If I wrote down the axiom of infinity for you, or wrote down all the axioms of ZFC and asked you to tell me which one implies infinity exists, you would be unable to.
Here's the facts. We are big with numbers in math. So it would be nice to know if it could be the case that one day someone will prove 1=0.
S(0)=/=0 is a trivial application of one of Peano's Axioms. See (3) at http://mathworld.wolfram.com/PeanosAxioms.html
Post by t***@gmail.com
The simplest method for formalizing numbers is with set theory.
Simpler still IMHO is to simply state Peano's Axioms at the beginning of a proof. Then you could dispense with AOI.
Post by t***@gmail.com
(1) Most people when inspecting the formal versions of the axioms of ZFC would not be able to spot which one has anything to do with infinity and (2) if we have a bunch of things we are willing to call sets then there must be a set consisting exactly of those sets we started with.
Does this make sense to you: there are numbers, which are specific sets, then we would like to consider "THE TOTALITY of all numbers" also a set.
In ZFC, everything is a set.

Dan

Visit my Math Blog at http://www.dcproof.wordpress.com
t***@gmail.com
2017-08-02 13:14:48 UTC
Raw Message
https://ibb.co/dyQREk

Which one of these has to do with infinity?

And why should it be considered "objectionable"?
Dan Christensen
2017-08-02 14:04:06 UTC
Raw Message
Post by t***@gmail.com
https://ibb.co/dyQREk
Which one of these has to do with infinity?
The so-called Axiom of Infinity postulates the existence of a set that includes the set of natural numbers (among other things potentially), though this is not be immediately apparent from the statement of the axiom alone.
Post by t***@gmail.com
And why should it be considered "objectionable"?
I have no problem with infinite sets, but IMHO the AOI in ZFC is a pedagogical nightmare and probably unnecessary. I prefer to simply state Peano's Axioms, which I find to much more intuitive than AOI. I guess it comes down to personal preference.

Dan

Visit my Math Blog at http://www.dcproof.wordpress.com
Peter Percival
2017-08-02 15:29:18 UTC
Raw Message
Post by Dan Christensen
I have no problem with infinite sets, but IMHO the AOI in ZFC is a
pedagogical nightmare and probably unnecessary.
If it were provable from the other axioms it would be unnecessary. It
isn't.
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
Dan Christensen
2017-08-02 15:53:22 UTC
Raw Message
Post by Peter Percival
Post by Dan Christensen
I have no problem with infinite sets, but IMHO the AOI in ZFC is a
pedagogical nightmare and probably unnecessary.
If it were provable from the other axioms it would be unnecessary. It
isn't.
An odd notion.

Dan
Peter Percival
2017-08-02 16:08:32 UTC
Raw Message
Post by Dan Christensen
Post by Peter Percival
Post by Dan Christensen
I have no problem with infinite sets, but IMHO the AOI in ZFC is a
pedagogical nightmare and probably unnecessary.
If it were provable from the other axioms it would be unnecessary. It
isn't.
An odd notion.
What specifically? I made two claims:

* If it were provable from the other axioms it would be unnecessary.

That seems clear. If it were provable it would not be needed as an
axiom. And

* It isn't provable from the other axioms.

That is also clear. There are models of ZF-Inf in which Inf is false.
So if ZF-Inf is consistent then Inf isn't a theorem of it.
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
Jim Burns
2017-08-02 16:12:10 UTC
Raw Message
On Wednesday, August 2, 2017 at 11:29:25 AM UTC-4,
Post by Peter Percival
Post by Dan Christensen
I have no problem with infinite sets, but IMHO
the AOI in ZFC is a pedagogical nightmare and
probably unnecessary.
If it were provable from the other axioms it would
be unnecessary. It isn't.
An odd notion.
Please think a little louder. Some of us on are
different continents.

For preference, think visibly on your screen, something
like
An odd notion _would be_
followed by something you consider an odd notion.

Some possible ways you could fill that in:
An odd notion would be
-- the existence of an infinite set.
-- the existence of any set.
-- the axiom of infinity.
-- the independence of the axiom of infinity.
-- trying to tell Dan Christensen anything.
Dan Christensen
2017-08-02 16:42:26 UTC
Raw Message
Post by Jim Burns
On Wednesday, August 2, 2017 at 11:29:25 AM UTC-4,
Post by Peter Percival
Post by Dan Christensen
I have no problem with infinite sets, but IMHO
the AOI in ZFC is a pedagogical nightmare and
probably unnecessary.
If it were provable from the other axioms it would
be unnecessary. It isn't.
An odd notion.
It is an odd notion that AOI not being provable from the other ZFC axioms would somehow have an bearing on whether or not AOI is necessary.

I hope this helps.

Dan
Peter Percival
2017-08-02 16:54:45 UTC
Raw Message
Post by Dan Christensen
Post by Jim Burns
On Wednesday, August 2, 2017 at 11:29:25 AM UTC-4,
Post by Peter Percival
Post by Dan Christensen
I have no problem with infinite sets, but IMHO
the AOI in ZFC is a pedagogical nightmare and
probably unnecessary.
If it were provable from the other axioms it would
be unnecessary. It isn't.
An odd notion.
It is an odd notion that AOI not being provable from the other ZFC axioms would somehow have an bearing on whether or not AOI is necessary.
If it were provable it would not be necessary to have it as an axiom.
(ok?) If it were not provable it would be necessary. Well almost,
because there might be some other axiom from which it is derivable. But
such an axiom would have to be added to ZF-Inf. (ok?)

It (or something of at least the same deductive strength) is necessary
if there are to be infinite sets. And everyone bar the strict finitists
thinks that there are are infinite sets.
Post by Dan Christensen
I hope this helps.
Dan
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
Dan Christensen
2017-08-02 20:16:21 UTC
Raw Message
Post by Peter Percival
Post by Dan Christensen
Post by Jim Burns
On Wednesday, August 2, 2017 at 11:29:25 AM UTC-4,
Post by Peter Percival
Post by Dan Christensen
I have no problem with infinite sets, but IMHO
the AOI in ZFC is a pedagogical nightmare and
probably unnecessary.
If it were provable from the other axioms it would
be unnecessary. It isn't.
An odd notion.
It is an odd notion that AOI not being provable from the other ZFC axioms would somehow have an bearing on whether or not AOI is necessary.
If it were provable it would not be necessary to have it as an axiom.
True.
Post by Peter Percival
If it were not provable it would be necessary.
I don't agree.
Post by Peter Percival
Well almost,
because there might be some other axiom from which it is derivable. But
such an axiom would have to be added to ZF-Inf. (ok?)
It (or something of at least the same deductive strength) is necessary
if there are to be infinite sets.
Again, my preferred approach is to introduce Peano's Axioms (or some equivalent) not in set theory, but as an initial assumption in proofs, as you might introduce the axioms of group theory.

Dan

Visit my Math Blog at http://www.dcproof.wordpress.com
Peter Percival
2017-08-02 21:25:55 UTC
Raw Message
Post by Dan Christensen
Post by Peter Percival
Post by Dan Christensen
Post by Jim Burns
On Wednesday, August 2, 2017 at 11:29:25 AM UTC-4,
Post by Peter Percival
Post by Dan Christensen
I have no problem with infinite sets, but IMHO
the AOI in ZFC is a pedagogical nightmare and
probably unnecessary.
If it were provable from the other axioms it would
be unnecessary. It isn't.
An odd notion.
It is an odd notion that AOI not being provable from the other ZFC axioms would somehow have an bearing on whether or not AOI is necessary.
If it were provable it would not be necessary to have it as an axiom.
True.
Post by Peter Percival
If it were not provable it would be necessary.
I don't agree.
How is the mathematics that deals with with infinite sets to be done?
Post by Dan Christensen
Post by Peter Percival
Well almost,
because there might be some other axiom from which it is derivable. But
such an axiom would have to be added to ZF-Inf. (ok?)
It (or something of at least the same deductive strength) is necessary
if there are to be infinite sets.
Again, my preferred approach is to introduce Peano's Axioms (or some equivalent) not in set theory, but as an initial assumption in proofs, as you might introduce the axioms of group theory.
Dan
Visit my Math Blog at http://www.dcproof.wordpress.com
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
Dan Christensen
2017-08-02 21:44:53 UTC
Raw Message
Post by Peter Percival
Post by Dan Christensen
Post by Peter Percival
Post by Dan Christensen
Post by Jim Burns
On Wednesday, August 2, 2017 at 11:29:25 AM UTC-4,
Post by Peter Percival
Post by Dan Christensen
I have no problem with infinite sets, but IMHO
the AOI in ZFC is a pedagogical nightmare and
probably unnecessary.
If it were provable from the other axioms it would
be unnecessary. It isn't.
An odd notion.
It is an odd notion that AOI not being provable from the other ZFC axioms would somehow have an bearing on whether or not AOI is necessary.
If it were provable it would not be necessary to have it as an axiom.
True.
Post by Peter Percival
If it were not provable it would be necessary.
I don't agree.
How is the mathematics that deals with with infinite sets to be done?
The set of natural numbers as defined by Peano's Axioms is infinite. Nothing would prevent you from assuming them in a proof. And nothing would prevent you from assuming the existence of an arbitrary infinite set in a proof. What more do you need?

Dan

Visit my Math Blog at http://www.dcproof.wordpress.com
Post by Peter Percival
Post by Dan Christensen
Post by Peter Percival
Well almost,
because there might be some other axiom from which it is derivable. But
such an axiom would have to be added to ZF-Inf. (ok?)
It (or something of at least the same deductive strength) is necessary
if there are to be infinite sets.
Again, my preferred approach is to introduce Peano's Axioms (or some equivalent) not in set theory, but as an initial assumption in proofs, as you might introduce the axioms of group theory.
Dan
Visit my Math Blog at http://www.dcproof.wordpress.com
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
Shobe, Martin
2017-08-03 01:28:29 UTC
Raw Message
Post by Dan Christensen
Post by Peter Percival
Post by Dan Christensen
Post by Peter Percival
Post by Dan Christensen
Post by Jim Burns
On Wednesday, August 2, 2017 at 11:29:25 AM UTC-4,
Post by Peter Percival
Post by Dan Christensen
I have no problem with infinite sets, but IMHO
the AOI in ZFC is a pedagogical nightmare and
probably unnecessary.
If it were provable from the other axioms it would
be unnecessary. It isn't.
An odd notion.
It is an odd notion that AOI not being provable from the other ZFC axioms would somehow have an bearing on whether or not AOI is necessary.
If it were provable it would not be necessary to have it as an axiom.
True.
Post by Peter Percival
If it were not provable it would be necessary.
I don't agree.
How is the mathematics that deals with with infinite sets to be done?
The set of natural numbers as defined by Peano's Axioms is infinite. Nothing would prevent you from assuming them in a proof. And nothing would prevent you from assuming the existence of an arbitrary infinite set in a proof. What more do you need?
If you assume the natural numbers exist you are assuming that the axiom
of infinity is true. Why include the remaining axioms when you've

Martin Shobe
Dan Christensen
2017-08-03 02:08:17 UTC
Raw Message
Post by Shobe, Martin
Post by Dan Christensen
Post by Peter Percival
Post by Dan Christensen
Post by Peter Percival
Post by Dan Christensen
Post by Jim Burns
On Wednesday, August 2, 2017 at 11:29:25 AM UTC-4,
Post by Peter Percival
Post by Dan Christensen
I have no problem with infinite sets, but IMHO
the AOI in ZFC is a pedagogical nightmare and
probably unnecessary.
If it were provable from the other axioms it would
be unnecessary. It isn't.
An odd notion.
It is an odd notion that AOI not being provable from the other ZFC axioms would somehow have an bearing on whether or not AOI is necessary.
If it were provable it would not be necessary to have it as an axiom.
True.
Post by Peter Percival
If it were not provable it would be necessary.
I don't agree.
How is the mathematics that deals with with infinite sets to be done?
The set of natural numbers as defined by Peano's Axioms is infinite. Nothing would prevent you from assuming them in a proof. And nothing would prevent you from assuming the existence of an arbitrary infinite set in a proof. What more do you need?
If you assume the natural numbers exist you are assuming that the axiom
of infinity is true.
How do you go from:

1. 0 in N
2. For all x in N: S(x) in x
3. For all x, y in N: [S(x)=S(y) => x=y]
4. For all x in N: S(x)=/=0
5. For all subsets P of N: [0 in N & For all x in P: [S(x) in P] => P=N]

To:

1. For all x: x not in phi
2. There exists I: [phi in I & For all x in I: [x U {x} in I]]

???

Dan

Visit my Math Blog at http://www.dcproof.wordpress.com
Shobe, Martin
2017-08-04 13:16:18 UTC
Raw Message
Post by Dan Christensen
Post by Shobe, Martin
Post by Dan Christensen
Post by Peter Percival
Post by Dan Christensen
Post by Peter Percival
Post by Dan Christensen
Post by Jim Burns
On Wednesday, August 2, 2017 at 11:29:25 AM UTC-4,
Post by Peter Percival
Post by Dan Christensen
I have no problem with infinite sets, but IMHO
the AOI in ZFC is a pedagogical nightmare and
probably unnecessary.
If it were provable from the other axioms it would
be unnecessary. It isn't.
An odd notion.
It is an odd notion that AOI not being provable from the other ZFC axioms would somehow have an bearing on whether or not AOI is necessary.
If it were provable it would not be necessary to have it as an axiom.
True.
Post by Peter Percival
If it were not provable it would be necessary.
I don't agree.
How is the mathematics that deals with with infinite sets to be done?
The set of natural numbers as defined by Peano's Axioms is infinite. Nothing would prevent you from assuming them in a proof. And nothing would prevent you from assuming the existence of an arbitrary infinite set in a proof. What more do you need?
If you assume the natural numbers exist you are assuming that the axiom
of infinity is true.
1. 0 in N
2. For all x in N: S(x) in x
This should be
2. For all x in N: S(x) in N
Post by Dan Christensen
3. For all x, y in N: [S(x)=S(y) => x=y]
4. For all x in N: S(x)=/=0
5. For all subsets P of N: [0 in N & For all x in P: [S(x) in P] => P=N]
1'. For all x: x not in phi
2'. There exists I: [phi in I & For all x in I: [x U {x} in I]]

Here, 0 = phi and S(x) = x U {x}.

That makes 2' the conjunction of 1 and 2.

Martin Shobe
Dan Christensen
2017-08-04 19:05:59 UTC
Raw Message
Post by Shobe, Martin
Post by Dan Christensen
Post by Shobe, Martin
Post by Dan Christensen
Post by Peter Percival
Post by Dan Christensen
Post by Peter Percival
Post by Dan Christensen
Post by Jim Burns
On Wednesday, August 2, 2017 at 11:29:25 AM UTC-4,
Post by Peter Percival
Post by Dan Christensen
I have no problem with infinite sets, but IMHO
the AOI in ZFC is a pedagogical nightmare and
probably unnecessary.
If it were provable from the other axioms it would
be unnecessary. It isn't.
An odd notion.
It is an odd notion that AOI not being provable from the other ZFC axioms would somehow have an bearing on whether or not AOI is necessary.
If it were provable it would not be necessary to have it as an axiom.
True.
Post by Peter Percival
If it were not provable it would be necessary.
I don't agree.
How is the mathematics that deals with with infinite sets to be done?
The set of natural numbers as defined by Peano's Axioms is infinite. Nothing would prevent you from assuming them in a proof. And nothing would prevent you from assuming the existence of an arbitrary infinite set in a proof. What more do you need?
If you assume the natural numbers exist you are assuming that the axiom
of infinity is true.
1. 0 in N
2. For all x in N: S(x) in x
This should be
2. For all x in N: S(x) in N
Post by Dan Christensen
3. For all x, y in N: [S(x)=S(y) => x=y]
4. For all x in N: S(x)=/=0
5. For all subsets P of N: [0 in N & For all x in P: [S(x) in P] => P=N]
1'. For all x: x not in phi
2'. There exists I: [phi in I & For all x in I: [x U {x} in I]]
Here, 0 = phi and S(x) = x U {x}.
That makes 2' the conjunction of 1 and 2.
I meant, how do you prove using ZFC-AOI and FOL that Peano's Axioms (as stated above) implies AOI. There is nothing to suggest in PA that 0 is the empty set or that S(x) = x U {x}.

Dan

Visit my Math Blog at http://www.dcproof.wordpress.com
Shobe, Martin
2017-08-04 20:11:30 UTC
Raw Message
Post by Dan Christensen
Post by Shobe, Martin
Post by Dan Christensen
Post by Shobe, Martin
Post by Dan Christensen
Post by Peter Percival
Post by Dan Christensen
Post by Peter Percival
Post by Dan Christensen
Post by Jim Burns
On Wednesday, August 2, 2017 at 11:29:25 AM UTC-4,
Post by Peter Percival
Post by Dan Christensen
I have no problem with infinite sets, but IMHO
the AOI in ZFC is a pedagogical nightmare and
probably unnecessary.
If it were provable from the other axioms it would
be unnecessary. It isn't.
An odd notion.
It is an odd notion that AOI not being provable from the other ZFC axioms would somehow have an bearing on whether or not AOI is necessary.
If it were provable it would not be necessary to have it as an axiom.
True.
Post by Peter Percival
If it were not provable it would be necessary.
I don't agree.
How is the mathematics that deals with with infinite sets to be done?
The set of natural numbers as defined by Peano's Axioms is infinite. Nothing would prevent you from assuming them in a proof. And nothing would prevent you from assuming the existence of an arbitrary infinite set in a proof. What more do you need?
If you assume the natural numbers exist you are assuming that the axiom
of infinity is true.
1. 0 in N
2. For all x in N: S(x) in x
This should be
2. For all x in N: S(x) in N
Post by Dan Christensen
3. For all x, y in N: [S(x)=S(y) => x=y]
4. For all x in N: S(x)=/=0
5. For all subsets P of N: [0 in N & For all x in P: [S(x) in P] => P=N]
1'. For all x: x not in phi
2'. There exists I: [phi in I & For all x in I: [x U {x} in I]]
Here, 0 = phi and S(x) = x U {x}.
That makes 2' the conjunction of 1 and 2.
I meant, how do you prove using ZFC-AOI and FOL that Peano's Axioms (as stated above) implies AOI. There is nothing to suggest in PA that 0 is the empty set or that S(x) = x U {x}.
Using the empty set for 0 and x U {x} for the successor function is the
standard construction of N.

Martin Shobe
Dan Christensen
2017-08-04 20:33:51 UTC
Raw Message
Post by Shobe, Martin
Post by Dan Christensen
Post by Shobe, Martin
Post by Dan Christensen
Post by Shobe, Martin
Post by Dan Christensen
Post by Peter Percival
Post by Dan Christensen
Post by Peter Percival
Post by Dan Christensen
Post by Jim Burns
On Wednesday, August 2, 2017 at 11:29:25 AM UTC-4,
Post by Peter Percival
Post by Dan Christensen
I have no problem with infinite sets, but IMHO
the AOI in ZFC is a pedagogical nightmare and
probably unnecessary.
If it were provable from the other axioms it would
be unnecessary. It isn't.
An odd notion.
It is an odd notion that AOI not being provable from the other ZFC axioms would somehow have an bearing on whether or not AOI is necessary.
If it were provable it would not be necessary to have it as an axiom.
True.
Post by Peter Percival
If it were not provable it would be necessary.
I don't agree.
How is the mathematics that deals with with infinite sets to be done?
The set of natural numbers as defined by Peano's Axioms is infinite. Nothing would prevent you from assuming them in a proof. And nothing would prevent you from assuming the existence of an arbitrary infinite set in a proof. What more do you need?
If you assume the natural numbers exist you are assuming that the axiom
of infinity is true.
1. 0 in N
2. For all x in N: S(x) in x
This should be
2. For all x in N: S(x) in N
Post by Dan Christensen
3. For all x, y in N: [S(x)=S(y) => x=y]
4. For all x in N: S(x)=/=0
5. For all subsets P of N: [0 in N & For all x in P: [S(x) in P] => P=N]
1'. For all x: x not in phi
2'. There exists I: [phi in I & For all x in I: [x U {x} in I]]
Here, 0 = phi and S(x) = x U {x}.
That makes 2' the conjunction of 1 and 2.
I meant, how do you prove using ZFC-AOI and FOL that Peano's Axioms (as stated above) implies AOI. There is nothing to suggest in PA that 0 is the empty set or that S(x) = x U {x}.
Using the empty set for 0 and x U {x} for the successor function is the
standard construction of N.
You are introducing additional axioms or assumptions without which, it seems you cannot prove the above implication.

Dan

Visit my Math Blog at http://www.dcproof.wordpress.com
FredJeffries
2017-08-04 20:53:34 UTC
Raw Message
Post by Dan Christensen
I meant, how do you prove using ZFC-AOI and FOL that Peano's Axioms (as stated above) implies AOI. There is nothing to suggest in PA that 0 is the empty set or that S(x) = x U {x}.
Use the Axiom of Replacement with f(0) = {} and f(S(n)) = f(n) U {f(n)}
Dan Christensen
2017-08-04 22:08:56 UTC
Raw Message
Post by FredJeffries
Post by Dan Christensen
I meant, how do you prove using ZFC-AOI and FOL that Peano's Axioms (as stated above) implies AOI. There is nothing to suggest in PA that 0 is the empty set or that S(x) = x U {x}.
Use the Axiom of Replacement with f(0) = {} and f(S(n)) = f(n) U {f(n)}
More assumptions that do not follow from Peano's Axioms.

Dan

Visit my Math Blog at http://www.dcproof.wordpress.com
FredJeffries
2017-08-05 01:16:41 UTC
Raw Message
Post by Dan Christensen
Post by FredJeffries
Post by Dan Christensen
I meant, how do you prove using ZFC-AOI and FOL that Peano's Axioms (as stated above) implies AOI. There is nothing to suggest in PA that 0 is the empty set or that S(x) = x U {x}.
Use the Axiom of Replacement with f(0) = {} and f(S(n)) = f(n) U {f(n)}
More assumptions that do not follow from Peano's Axioms.
Thus, you admit that you do not actually know what ZFC is.

http://mathworld.wolfram.com/AxiomofReplacement.html
http://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html
https://en.wikipedia.org/wiki/Axiom_schema_of_replacement
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
Dan Christensen
2017-08-05 01:37:31 UTC
Raw Message
Post by FredJeffries
Post by Dan Christensen
Post by FredJeffries
Post by Dan Christensen
I meant, how do you prove using ZFC-AOI and FOL that Peano's Axioms (as stated above) implies AOI. There is nothing to suggest in PA that 0 is the empty set or that S(x) = x U {x}.
Use the Axiom of Replacement with f(0) = {} and f(S(n)) = f(n) U {f(n)}
More assumptions that do not follow from Peano's Axioms.
Thus, you admit that you do not actually know what ZFC is.
http://mathworld.wolfram.com/AxiomofReplacement.html
http://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html
https://en.wikipedia.org/wiki/Axiom_schema_of_replacement
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
I'm certainly no expert in ZFC theory, but perhaps you do not realize that, in set theory, you cannot define sets and functions willy-nilly. If they are not explicitly defined in the axioms of set theory, you must explicitly assume or prove their existence. In this case, you must explicitly assume or prove the existence of your function f: N --> ??? If you cannot prove it, you must explicitly assume it, i.e. introduce assumptions in addition to Peano's.

Dan

Visit my Math Blog at http://www.dcproof.wordpress.com

Peter Percival
2017-08-03 05:48:22 UTC
Raw Message
Post by Dan Christensen
Post by Peter Percival
How is the mathematics that deals with with infinite sets to be done?
The set of natural numbers as defined by Peano's Axioms is infinite.
How do you know that there is something that satisfies the definition?

Do you recall (recently, in another thread) writing about the need to
construct, not just define, a mathematical object, and I asked what you
meant by construct? It turned out that "construct" meant "define and
prove the existence of".
Post by Dan Christensen
Nothing would prevent you from assuming them in a proof. And nothing
would prevent you from assuming the existence of an arbitrary
infinite set in a proof. What more do you need?
Undischarged assumptions in proofs are called axioms.
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
Dan Christensen
2017-08-03 15:05:19 UTC
Raw Message
Post by Peter Percival
Post by Dan Christensen
Post by Peter Percival
How is the mathematics that deals with with infinite sets to be done?
The set of natural numbers as defined by Peano's Axioms is infinite.
How do you know that there is something that satisfies the definition?
Peano's Axioms are held to be self-evident truths about the natural numbers based on thousands of years of intensive use in diverse cultures.
Post by Peter Percival
Do you recall (recently, in another thread) writing about the need to
construct, not just define, a mathematical object, and I asked what you
meant by construct? It turned out that "construct" meant "define and
prove the existence of".
You have to start with some original axioms postulating the existence of some object(s), but these axioms need not be axioms of set theory. And Peano's Axioms seem like the logical starting point for most if not all of mathematics.
Post by Peter Percival
Post by Dan Christensen
Nothing would prevent you from assuming them in a proof. And nothing
would prevent you from assuming the existence of an arbitrary
infinite set in a proof. What more do you need?
Undischarged assumptions in proofs are called axioms.
Undischarged assumptions in proofs need not be axioms of set theory.

Dan
Peter Percival
2017-08-03 17:04:14 UTC
Raw Message
Post by Dan Christensen
And Peano's Axioms seem like the logical starting point for most if
not all of mathematics.
Most of arithmetic, maybe, but most of mathematics?
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
Dan Christensen
2017-08-03 17:20:07 UTC
Raw Message
Post by Peter Percival
Post by Dan Christensen
And Peano's Axioms seem like the logical starting point for most if
not all of mathematics.
Most of arithmetic, maybe, but most of mathematics?
Yes. It is possible to construct the integers, rational, real and complex numbers starting from Peano's Axioms. I'm guessing that would cover at least 99.8% of all published mathematics.

Dan

Visit my Math Blog at http://www.dcproof.wordpress.com
bassam king karzeddin
2017-08-03 09:57:07 UTC
Raw Message
Post by Dan Christensen
On Wednesday, August 2, 2017 at 11:29:25 AM UTC-4,
The set of natural numbers as defined by Peano's Axioms is infinite. Nothing would prevent you from assuming them in a proof. And nothing would prevent you from assuming the existence of an arbitrary infinite set in a proof. What more do you need?
**********************************************
But you need to know that the set of natural numbers doesn't exist, nor any other set that is assumed to have infinite terms for sure

BKK
Post by Dan Christensen
Dan
Visit my Math Blog at http://www.dcproof.wordpress.com
Dan Christensen
2017-08-03 15:16:25 UTC
Raw Message
Post by bassam king karzeddin
Post by Dan Christensen
On Wednesday, August 2, 2017 at 11:29:25 AM UTC-4,
The set of natural numbers as defined by Peano's Axioms is infinite. Nothing would prevent you from assuming them in a proof. And nothing would prevent you from assuming the existence of an arbitrary infinite set in a proof. What more do you need?
**********************************************
But you need to know that the set of natural numbers doesn't exist, nor any other set that is assumed to have infinite terms for sure
Just like 40 degree angles don't exist, right, BKK? You are a crank and a troll. You are wasting your time here.
Post by bassam king karzeddin
Post by Dan Christensen
Dan
Visit my Math Blog at http://www.dcproof.wordpress.com
bassam king karzeddin
2017-08-03 15:48:33 UTC
Raw Message
Post by Dan Christensen
Post by bassam king karzeddin
Post by Dan Christensen
On Wednesday, August 2, 2017 at 11:29:25 AM UTC-4,
The set of natural numbers as defined by Peano's Axioms is infinite. Nothing would prevent you from assuming them in a proof. And nothing would prevent you from assuming the existence of an arbitrary infinite set in a proof. What more do you need?
**********************************************
But you need to know that the set of natural numbers doesn't exist, nor any other set that is assumed to have infinite terms for sure
Just like 40 degree angles don't exist, right, BKK? You are a crank and a troll. You are wasting your time here.
Post by bassam king karzeddin
Post by Dan Christensen
Dan
Visit my Math Blog at http://www.dcproof.wordpress.com
You still think confidently that (40) degrees angle exists, or you may so naively think that I am trolling, I swear that angle doesn't exist and will never exist for sure

If you don't get my published proofs here at sci.math, then go and ask all the mathematicians on earth to create it for you in any existing triangle with known exact sides

This angle and much more infinitely many angles (in current mathematics language) exists only in that called the perfect circle, but so, unfortunately, the very bad news for mathematicians, that the perfect circle was proven as non-existent (both in mind and also in physical reality), but it does exist indeed only in the very poor minds calling themselves as mathematicians

And you would never get it since like anyone you saw it marked at your Protractor

And certainly, one is impossible to progress in maths if he can't overcome those newly published issues

And once I did create the doubt, then wait and see in the near future how the secretive researchers or the Wikipedia writers would soon establish it (if they were allowed), claiming and fabricating very old references as usual, for sure

Actually, I found that the angle analysis is the best way to refute the real existence of both (algebraic and transcendental) numbers since they didn't establish yet something like epsilon and delta that had been made to manufacture those many fiction non-existing alleged real numbers that live in mind only

And if you and all the mathematicians on earth can't show only one angle then you have no right to claim bullshit names on others

Bassam King Karzeddin
8/3/17
Dan Christensen
2017-08-03 17:09:51 UTC
Raw Message
Post by bassam king karzeddin
Post by Dan Christensen
Post by bassam king karzeddin
Post by Dan Christensen
On Wednesday, August 2, 2017 at 11:29:25 AM UTC-4,
The set of natural numbers as defined by Peano's Axioms is infinite. Nothing would prevent you from assuming them in a proof. And nothing would prevent you from assuming the existence of an arbitrary infinite set in a proof. What more do you need?
**********************************************
But you need to know that the set of natural numbers doesn't exist, nor any other set that is assumed to have infinite terms for sure
Just like 40 degree angles don't exist, right, BKK? You are a crank and a troll. You are wasting your time here.
Post by bassam king karzeddin
Post by Dan Christensen
Dan
Visit my Math Blog at http://www.dcproof.wordpress.com
You still think confidently that (40) degrees angle exists,
So does everyone but you, BKK.
Post by bassam king karzeddin
or you may so naively think that I am trolling, I swear that angle doesn't exist and will never exist for sure
Pathetic.
Post by bassam king karzeddin
If you don't get my published proofs here at sci.math, then go and ask all the mathematicians on earth to create it for you in any existing triangle with known exact sides
A triangle of sides 1, sin 40 and cos 40 has angles of 90, 50 and 40 degrees. Deal with it.
Post by bassam king karzeddin
This angle and much more infinitely many angles (in current mathematics language) exists only in that called the perfect circle, but so, unfortunately, the very bad news for mathematicians, that the perfect circle was proven as non-existent (both in mind and also in physical reality),
[snip]

No 40 degree angles. Now, no circles! What next? No numbers? You are looking like a complete idiot here, BKK.
Post by bassam king karzeddin
And certainly, one is impossible to progress in maths if he can't overcome those newly published issues
HA, HA!!! How much progress have you made in your goofy system. You still cannot even establish the most basic results of basic arithmetic.
Post by bassam king karzeddin
And once I did create the doubt, then wait and see in the near future how the secretive researchers or the Wikipedia writers would soon establish it (if they were allowed), claiming and fabricating very old references as usual, for sure
Good luck creating doubts about 40 degree angles and circles.

Dan
Dan Christensen
2017-08-02 20:29:33 UTC
Raw Message
Post by Peter Percival
Post by Dan Christensen
Post by Jim Burns
On Wednesday, August 2, 2017 at 11:29:25 AM UTC-4,
Post by Peter Percival
Post by Dan Christensen
I have no problem with infinite sets, but IMHO
the AOI in ZFC is a pedagogical nightmare and
probably unnecessary.
If it were provable from the other axioms it would
be unnecessary. It isn't.
An odd notion.
It is an odd notion that AOI not being provable from the other ZFC axioms would somehow have an bearing on whether or not AOI is necessary.
If it were provable it would not be necessary to have it as an axiom.
True.
Post by Peter Percival
If it were not provable it would be necessary.
I don't agree.
Post by Peter Percival
Well almost,
because there might be some other axiom from which it is derivable. But
such an axiom would have to be added to ZF-Inf. (ok?)
It (or something of at least the same deductive strength) is necessary
if there are to be infinite sets.
Again, my preferred approach is to introduce Peano's Axioms (or some equivalent) not as an axiom of set theory, but as an initial assumption in proofs, as you might introduce the axioms of group theory.

Dan

Visit my Math Blog at http://www.dcproof.wordpress.com
Jim Burns
2017-08-02 17:23:57 UTC
Raw Message
On Wednesday, August 2, 2017 at 12:12:16 PM UTC-4,
Post by Jim Burns
On Wednesday, August 2, 2017 at 11:29:25 AM UTC-4,
Post by Peter Percival
Post by Dan Christensen
I have no problem with infinite sets, but IMHO
the AOI in ZFC is a pedagogical nightmare and
probably unnecessary.
If it were provable from the other axioms it would
be unnecessary. It isn't.
An odd notion.
It is an odd notion that AOI not being provable
from the other ZFC axioms would somehow have an
bearing on whether or not AOI is necessary.
I hope this helps.
It does help. Thanks.

----
If we assume
(Ax) x + 0 = x
(Ax,y) x + Sy = S(x + y)
then it's not necessary to assume in addition that
SS0 + SS0 = SSSS0

I'm pretty confident that this is the kind of thing
that Peter Percival means.

----
Let's consider a _theory_ Thr as some class Frm of
formulas in some language Lng which is closed under
some inference rules Rul .

If we can describe Frm as the smallest class of formulas
closed under Rul and containing some class of formulas Axm,
then describing Rul and Axm describes Frm, even though
Frm is typically infinite. This is a more general use
of induction.

But there may be more than one class of formulas which
could be Axm and still describe the same Frm.
The class Frm itself, for example, though that's
extremely uninteresting.

A formula (such as one stating that every set is strictly
smaller than its power set) is _unnecessary_ if it can
be removed from Axm without changing Frm. All of the
non-axiom theorems of Thr are unnecessary in this sense.
We've included them in our description by saying Frm
is closed under Rul.

It's certainly possible to remove Infinity from ZFC,
so it's not necessary in that sense. But if one does that,
one now has a _different_ Frm that one is talking about.

There's no inherent logical error in including unnecessary
formulas in Axm, not that I'm aware of. As I said,
we could include _all_ of Frm in Axm. But the more concise
we make Axm, the less clutter there is to obstruct our
view of what we really are talking about.

We could add Cantor's diagonal theorem to ZFC as an
axiom, and nothing terrible would happen. But we have
-- in effect -- already included it. Stating it
explicitly would just distract.

Peter Percival's point is that this is *NOT* the
case for the Axiom of Infinity. If we removed it,
yes, we would have _something_ , but we would have
something _different_ .
Dan Christensen
2017-08-02 16:10:00 UTC
Raw Message
Post by Peter Percival
Post by Dan Christensen
I have no problem with infinite sets, but IMHO the AOI in ZFC is a
pedagogical nightmare and probably unnecessary.
If it were provable from the other axioms it would be unnecessary. It
isn't.
So, if were NOT provable from the other axioms, then it may or may not be necessary. Ummmm... OK.

Dan
FromTheRafters
2017-08-02 18:17:55 UTC
Raw Message
Post by Dan Christensen
Post by Peter Percival
Post by Dan Christensen
I have no problem with infinite sets, but IMHO the AOI in ZFC is a
pedagogical nightmare and probably unnecessary.
If it were provable from the other axioms it would be unnecessary. It
isn't.
So, if were NOT provable from the other axioms, then it may or may not be
necessary. Ummmm... OK.
Dan
If deemed necessary, it wouldn't need to be an axiom if it could be a
theorem with a proof using the already existing axioms for that system.
Peter Percival
2017-08-02 15:28:05 UTC
Raw Message
Post by t***@gmail.com
https://ibb.co/dyQREk
Which one of these has to do with infinity?
5th
Post by t***@gmail.com
And why should it be considered "objectionable"?
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
Peter Percival
2017-08-01 21:54:30 UTC
Raw Message
[...] if we have a bunch of things we are willing to call sets then
theremust be a set consisting exactly of those sets we started with.
The collection of all the sets in the cumulative hierarchy does not
constitute a set.
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
Dan Christensen
2017-08-02 02:31:51 UTC