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Topic: Answer to Dik T. Winter
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mueckenh@rz.fh-augsburg.de

Posts: 13,482
Registered: 1/29/05
Re: Natural numbers are uniquely defined
Posted: May 30, 2009 4:05 PM
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On 30 Mai, 02:56, "Peter Webb" <webbfam...@DIESPAMDIEoptusnet.com.au>
wrote:
> >> Grant the existence of two natural numbers m and n such that m/n = sqrt
> >> (2). Then falsify it.
> >> Grant the existence of a largest natural. Then falsify it.
> >> Grant the existence of a largest prime number. Then falsify it.
> >> Grant the existence of all natural numbers. Then falsify it.

>
> >> All these proofs are proofs by contradiction.
>
> >> *************************
>
> >> How do you falsify the existence of the set of all Natural numbers in ZF
> >> ?
> >> ZF includes an axiom of infinity, which pretty much directly guarantees
> >> that
> >> there is an infinite set of all finite ordinals.

>
> > What about classical arithmetics with an axiom that sqrt(2) is a
> > rational number?

>
> This does not answer my question.
>
> But I will answer yours for you. If you create a version of "classical" (=
> "standard" ?) arithmetic with an axiom that sqrt(2) is rational, it would > be
> inconsistent, and hence useless.


Same with the axiom of infinity: ?There exists a complete linear
infinite set? is a self-contradictory similar to ?there exists a pair
of natural numbers, a and b, such that b^2 = 2a^2.
>
> Now how about answering my question. How do you falsify the existence of the
> set of all Natural numbers in ZF, as you claimed you could?


It is simple: ... classical logic was abstracted from the mathematics
of finite sets and their subsets .... Forgetful of this limited
origin, one afterwards mistook that logic for something above and
prior to all mathematics, and finally applied it, without
justification, to the mathematics of infinite sets. [Hermann Weyl,
"Mathematics and logic: A brief survey serving as a preface to a
review of The Philosophy of Bertrand Russell", American Mathematical
Monthly 53: 2?13]

Show me a complete finite linear set that does not allow for
quantifier reversal.
En Am: m =< n <==> Am En m =< n [*] .

Therefore: Either [*] holds or the set is not complete but allows for
extension.
Then we have only
En Am: m =< n ==> Am En m =< n [**]
because not all elements are readily available.
That is called a potentially infinite set. But in this case there is
no chance to prove uncountability.
This had already been recognized by the late Alexander Zenkin, one of
the brave scientists who dared to condemn this hypocritical
behaviour:
Cantor's 'paradise' as well as all modern axiomatic set theory is
based on the (self-contradictory) concept of actual infinity. Cantor
emphasized plainly and constantly that all transfinite objects of his
set theory are based on the actual infinity. Modern AST-people try to
persuade us to believe that the AST does not use actual infinity. It
is an intentional and blatant lie, since if infinite sets, X and N,
are potential, then the uncountability of the continuum becomes
unprovable, but without the notorious uncountablity of continuum the
modern AST as a whole transforms into a long twaddle about nothing.

Resume: The internal contradiction in set theory is veiled by mixing
up potential and actual infinity. That is the reason why set theorists
usually refuse to specify which infinity they apply. Most even pretend
(or profess) not to know the difference.

Regards, WM


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mueckenh@rz.fh-augsburg.de
6/11/09
Read Re: Answer to Dik T. Winter
Virgil
6/11/09
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Dik T. Winter
6/12/09
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mueckenh@rz.fh-augsburg.de
6/12/09
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Virgil
6/19/09
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Dik T. Winter
6/19/09
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mueckenh@rz.fh-augsburg.de
6/19/09
Read Re: Answer to Dik T. Winter
Virgil
6/22/09
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Dik T. Winter
6/25/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/25/09
Read Re: Answer to Dik T. Winter
Virgil
6/30/09
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Dik T. Winter
6/30/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/30/09
Read Re: Answer to Dik T. Winter
MeAmI.org
6/30/09
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Virgil
7/1/09
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Dik T. Winter
7/2/09
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G. Frege
7/2/09
Read Re: Answer to Dik T. Winter
Dik T. Winter
7/2/09
Read Re: Answer to Dik T. Winter
herb z
7/2/09
Read Re: Answer to Dik T. Winter
Dik T. Winter
7/2/09
Read Re: Answer to Dik T. Winter
herb z
7/2/09
Read Re: Answer to Dik T. Winter
G. Frege
7/3/09
Read Re: Answer to Dik T. Winter
Aatu Koskensilta
7/3/09
Read Re: Answer to Dik T. Winter
Daryl McCullough
7/2/09
Read Re: Answer to Dik T. Winter
G. Frege
7/2/09
Read Re: Answer to Dik T. Winter
G. Frege
7/2/09
Read Re: Answer to Dik T. Winter
G. Frege
7/2/09
Read Re: Answer to Dik T. Winter
Jack Markan
7/2/09
Read Re: Answer to Dik T. Winter
G. Frege
7/2/09
Read Re: Answer to Dik T. Winter
Jack Markan
7/2/09
Read Re: Answer to Dik T. Winter
G. Frege
7/2/09
Read Re: Answer to Dik T. Winter
Jack Markan
7/3/09
Read Re: Answer to Dik T. Winter
Dik T. Winter
7/3/09
Read Re: Answer to Dik T. Winter
G. Frege
7/3/09
Read Re: Answer to Dik T. Winter
Dik T. Winter
7/3/09
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G. Frege
7/4/09
Read Re: Answer to Dik T. Winter
Aatu Koskensilta
7/6/09
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Dik T. Winter
7/6/09
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G. Frege
7/6/09
Read Re: Answer to Dik T. Winter
Dik T. Winter
7/6/09
Read Re: Answer to Dik T. Winter
Jesse F. Hughes
7/3/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
7/3/09
Read Re: Answer to Dik T. Winter
Virgil
7/3/09
Read Re: Answer to Dik T. Winter
Ralf Bader
7/2/09
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G. Frege
7/2/09
Read Re: Answer to Dik T. Winter
Virgil
7/2/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
7/2/09
Read Re: Answer to Dik T. Winter
ross.finlayson@gmail.com
7/2/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
7/2/09
Read Re: Answer to Dik T. Winter
Jack Markan
7/2/09
Read Re: Answer to Dik T. Winter
Jack Markan
7/2/09
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Virgil
7/2/09
Read Re: Answer to Dik T. Winter
ross.finlayson@gmail.com
7/2/09
Read Re: Answer to Dik T. Winter
Jack Markan
7/2/09
Read Re: Answer to Dik T. Winter
ross.finlayson@gmail.com
7/6/09
Read Re: Answer to Dik T. Winter
Jack Markan
7/6/09
Read Re: Answer to Dik T. Winter
ross.finlayson@gmail.com
7/6/09
Read Re: Answer to Dik T. Winter
Jack Markan
7/6/09
Read Re: Answer to Dik T. Winter
ross.finlayson@gmail.com
7/6/09
Read Re: Answer to Dik T. Winter
Jack Markan
6/8/09
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mueckenh@rz.fh-augsburg.de
6/8/09
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Virgil
6/9/09
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Jack Markan
6/9/09
Read Re: Answer to Dik T. Winter
Jack Markan
6/9/09
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Virgil
6/11/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/11/09
Read Re: Answer to Dik T. Winter
Virgil
6/11/09
Read Re: Answer to Dik T. Winter
William Hughes
6/11/09
Read Re: Answer to Dik T. Winter
Virgil
6/11/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/11/09
Read Re: Answer to Dik T. Winter
Virgil
6/11/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/11/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/11/09
Read Re: Answer to Dik T. Winter
Virgil
6/11/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/11/09
Read Re: Answer to Dik T. Winter
Virgil
6/12/09
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herb z
6/12/09
Read Re: Answer to Dik T. Winter
Virgil
6/12/09
Read Re: Answer to Dik T. Winter
Owen Jacobson
6/12/09
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Virgil
6/12/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/12/09
Read Re: Answer to Dik T. Winter
Virgil
6/11/09
Read Re: Answer to Dik T. Winter
Virgil
6/11/09
Read Re: Answer to Dik T. Winter
Dik T. Winter
6/11/09
Read Re: Answer to Dik T. Winter
William Hughes
6/11/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/11/09
Read Re: Answer to Dik T. Winter
YBM
6/11/09
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Virgil
6/11/09
Read Re: Answer to Dik T. Winter
Dik T. Winter
6/12/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/12/09
Read Re: Answer to Dik T. Winter
Virgil
6/12/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/12/09
Read Re: Answer to Dik T. Winter
Virgil
6/19/09
Read Re: Answer to Dik T. Winter
Dik T. Winter
6/19/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/19/09
Read Re: Answer to Dik T. Winter
Virgil
6/22/09
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Dik T. Winter
6/25/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/25/09
Read Re: Answer to Dik T. Winter
Virgil
6/30/09
Read Re: Answer to Dik T. Winter
Dik T. Winter
6/30/09
Read Re: Answer to Dik T. Winter
Virgil
6/30/09
Read Re: Answer to Dik T. Winter
Guest
6/30/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
7/1/09
Read Re: Answer to Dik T. Winter
Dik T. Winter
6/11/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/11/09
Read Re: Answer to Dik T. Winter
Virgil
6/3/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/3/09
Read Re: Answer to Dik T. Winter
Virgil
6/3/09
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Dik T. Winter
6/7/09
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mueckenh@rz.fh-augsburg.de
6/7/09
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Virgil
6/11/09
Read Re: Answer to Dik T. Winter
Dik T. Winter
6/3/09
Read Re: Answer to Dik T. Winter
george
5/29/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
5/29/09
Read Re: Answer to Dik T. Winter
Virgil
5/30/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
5/30/09
Read Re: Answer to Dik T. Winter
Virgil
5/31/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
5/31/09
Read Re: Answer to Dik T. Winter
Virgil
5/31/09
Read Re: Answer to Dik T. Winter
Guest
5/27/09
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Virgil
5/28/09
Read Who introduced false logic?
mueckenh@rz.fh-augsburg.de
5/28/09
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Virgil
5/30/09
Read Re: Who introduced false logic?
mueckenh@rz.fh-augsburg.de
5/30/09
Read Re: Who introduced false logic?
Virgil
5/30/09
Read Re: Who introduced false logic?
Virgil
5/30/09
Read Re: Answer to Dik T. Winter
Virgil
5/30/09
Read Re: Answer to Dik T. Winter
Virgil
5/30/09
Read Re: Answer to Dik T. Winter
Ralf Bader
5/27/09
Read Natural numbers are uniquely defined
mueckenh@rz.fh-augsburg.de
5/27/09
Read Re: Natural numbers are uniquely defined
David C. Ullrich
5/27/09
Read Re: Natural numbers are uniquely defined
Virgil
5/27/09
Read Re: Natural numbers are uniquely defined
Guest
5/27/09
Read Re: Natural numbers are uniquely defined
mueckenh@rz.fh-augsburg.de
5/28/09
Read Re: Natural numbers are uniquely defined
mueckenh@rz.fh-augsburg.de
5/28/09
Read Re: Natural numbers are uniquely defined
Virgil
5/29/09
Read Re: Natural numbers are uniquely defined
Peter Webb
5/29/09
Read Re: Natural numbers are uniquely defined
Virgil
5/29/09
Read Re: Natural numbers are uniquely defined
mueckenh@rz.fh-augsburg.de
5/29/09
Read Re: Natural numbers are uniquely defined
Virgil
5/29/09
Read Re: Natural numbers are uniquely defined
Peter Webb
5/30/09
Read Re: Natural numbers are uniquely defined
mueckenh@rz.fh-augsburg.de
5/30/09
Read Re: Natural numbers are uniquely defined
Virgil
5/30/09
Read Re: Natural numbers are uniquely defined
Peter Webb
5/31/09
Read Re: Natural numbers are uniquely defined
mueckenh@rz.fh-augsburg.de
5/31/09
Read Re: Natural numbers are uniquely defined
Virgil
5/31/09
Read Re: Natural numbers are uniquely defined
mueckenh@rz.fh-augsburg.de
5/31/09
Read Re: Natural numbers are uniquely defined
Peter Webb
5/31/09
Read Re: Natural numbers are uniquely defined
Virgil
6/1/09
Read Re: Natural numbers are uniquely defined
mueckenh@rz.fh-augsburg.de
6/1/09
Read Re: Natural numbers are uniquely defined
David Bernier
6/1/09
Read Re: Natural numbers are uniquely defined
Jack Markan
6/1/09
Read Re: Natural numbers are uniquely defined
Virgil
6/2/09
Read Re: Natural numbers are uniquely defined
george
6/1/09
Read Re: Natural numbers are uniquely defined
mueckenh@rz.fh-augsburg.de
6/1/09
Read Re: Natural numbers are uniquely defined
Virgil
6/2/09
Read Re: Natural numbers are uniquely defined
george
6/2/09
Read Re: Natural numbers are uniquely defined
george
6/2/09
Read Re: Natural numbers are uniquely defined
george
6/3/09
Read Re: Natural numbers are uniquely defined
george
6/12/09
Read Re: Answer to Dik T. Winter
Guest
2/5/13
Read Re: Answer to Dik T. Winter
6/14/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/14/09
Read Re: Answer to Dik T. Winter
Virgil
6/14/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/14/09
Read Re: Answer to Dik T. Winter
Virgil
6/15/09
Read Re: Answer to Dik T. Winter
Owen Jacobson
6/15/09
Read Re: Answer to Dik T. Winter
Virgil
6/15/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/15/09
Read Re: Answer to Dik T. Winter
Owen Jacobson
6/15/09
Read Re: Answer to Dik T. Winter
Virgil
6/15/09
Read Re: Answer to Dik T. Winter
Virgil
6/16/09
Read Re: Answer to Dik T. Winter
MeAmI.org
6/16/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/16/09
Read Re: Answer to Dik T. Winter
Virgil
6/18/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/18/09
Read Re: Answer to Dik T. Winter
Virgil
6/20/09
Read Re: Answer to Dik T. Winter
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