Discussion:
Isn't infinity (in mathematics) actually a flawed concept?
bassam king karzeddin
2017-04-15 12:35:42 UTC
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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).
w***@gmail.com
2017-04-19 19:06:56 UTC
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
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
bassam king karzeddin
2017-04-15 16:36:32 UTC
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
WM
2017-04-15 16:16:39 UTC
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
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
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
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
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
Shut the fuck up mathforum.org imbecile.
bassam king karzeddin
2017-04-16 06:02:33 UTC
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
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
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
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
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