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Topic: Answer to Dik T. Winter
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Virgil

Posts: 311
Registered: 5/26/09
Re: Natural numbers are uniquely defined
Posted: May 30, 2009 5:16 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article
<4f20ac0a-a6b7-4a20-8eca-84a63b1f69b6@c19g2000yqc.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:


> >
> > 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: ³There exists a complete linear
> infinite set² is a self-contradictory similar to ³there exists a pair
> of natural numbers, a and b, such that b^2 = 2a^2.


WM keeps claiming this but never manages to prove it. All of his
attempts at proofs require assuming a priori and without proof that no
infinite set can exist.



> >
> > 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: 2­13]


So from what cathedra was Weyl speaking?
Arguing from citing authorities may work in law courts, but carries
little weight mathematics.
>
> Show me a complete finite linear set that does not allow for
> quantifier reversal.
> En Am: m =< n <==> Am En m =< n [*] .


Show me that every infinite well ordered set does allow it.
>
> Therefore: Either [*] holds or the set is not complete but allows for
> extension.


Or the set is infintie, well-ordered, and has no maximal member.

> Then we have only
> En Am: m =< n ==> Am En m =< n [**]
> because not all elements are readily available.


Any set in a sane set theory has all members equally "available".


> That is called a potentially infinite set.

That is called nonsense in set theories, as is much of WM's
MathUnrealism.

--
Virgil


Date Subject Author
5/27/09
Read Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
5/27/09
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Dik T. Winter
5/27/09
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mueckenh@rz.fh-augsburg.de
5/27/09
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5/27/09
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Virgil
5/27/09
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5/27/09
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Virgil
5/27/09
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Virgil
5/28/09
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mueckenh@rz.fh-augsburg.de
5/28/09
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Virgil
5/28/09
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Dik T. Winter
5/28/09
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5/28/09
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Jesse F. Hughes
5/29/09
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Dik T. Winter
5/29/09
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G. Frege
5/29/09
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Dik T. Winter
5/30/09
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G. Frege
5/30/09
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Jesse F. Hughes
6/2/09
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Dik T. Winter
5/30/09
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Jesse F. Hughes
5/30/09
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6/1/09
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6/1/09
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Jesse F. Hughes
6/1/09
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6/2/09
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6/2/09
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6/2/09
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6/11/09
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6/11/09
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Virgil
6/11/09
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6/11/09
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6/11/09
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Virgil
6/11/09
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6/11/09
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Guest
6/11/09
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6/11/09
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Virgil
6/11/09
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6/12/09
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6/12/09
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Virgil
6/12/09
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6/12/09
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Virgil
6/12/09
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William Hughes
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Virgil
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Virgil
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6/13/09
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Virgil
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Virgil
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Virgil
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6/14/09
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6/13/09
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6/17/09
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6/17/09
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6/17/09
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6/17/09
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6/17/09
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6/17/09
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6/17/09
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6/17/09
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6/18/09
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6/18/09
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6/18/09
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6/18/09
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6/18/09
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6/19/09
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6/19/09
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6/19/09
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6/19/09
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6/19/09
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6/19/09
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6/19/09
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6/19/09
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6/19/09
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6/19/09
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6/19/09
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6/20/09
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6/20/09
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6/20/09
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6/20/09
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6/20/09
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6/20/09
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6/20/09
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6/20/09
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6/20/09
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6/20/09
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6/2/09
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6/2/09
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6/3/09
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6/3/09
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6/3/09
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6/3/09
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6/3/09
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6/3/09
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6/3/09
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6/3/09
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6/7/09
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6/10/09
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6/25/09
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mueckenh@rz.fh-augsburg.de
6/25/09
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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
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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
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Dik T. Winter
7/2/09
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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
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Aatu Koskensilta
7/3/09
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Daryl McCullough
7/2/09
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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
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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
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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
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Aatu Koskensilta
7/6/09
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Dik T. Winter
7/6/09
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G. Frege
7/6/09
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Dik T. Winter
7/6/09
Read Re: Answer to Dik T. Winter
Jesse F. Hughes
7/3/09
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mueckenh@rz.fh-augsburg.de
7/3/09
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Virgil
7/3/09
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Ralf Bader
7/2/09
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G. Frege
7/2/09
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Virgil
7/2/09
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mueckenh@rz.fh-augsburg.de
7/2/09
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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
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ross.finlayson@gmail.com
7/2/09
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Jack Markan
7/2/09
Read Re: Answer to Dik T. Winter
ross.finlayson@gmail.com
7/6/09
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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
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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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William Hughes
6/11/09
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Virgil
6/11/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/11/09
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Virgil
6/11/09
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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
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Virgil
6/12/09
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herb z
6/12/09
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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
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Virgil
6/11/09
Read Re: Answer to Dik T. Winter
Virgil
6/11/09
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Dik T. Winter
6/11/09
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William Hughes
6/11/09
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mueckenh@rz.fh-augsburg.de
6/11/09
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YBM
6/11/09
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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
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
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Dik T. Winter
6/19/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/19/09
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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
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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?
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5/28/09
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5/30/09
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5/30/09
Read Re: Who introduced false logic?
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5/30/09
Read Re: Who introduced false logic?
Virgil
5/30/09
Read Re: Answer to Dik T. Winter
Virgil
5/30/09
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Virgil
5/30/09
Read Re: Answer to Dik T. Winter
Ralf Bader
5/27/09
Read Natural numbers are uniquely defined
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5/27/09
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David C. Ullrich
5/27/09
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Virgil
5/27/09
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5/27/09
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5/28/09
Read Re: Natural numbers are uniquely defined
mueckenh@rz.fh-augsburg.de
5/28/09
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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
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5/29/09
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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
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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
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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
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Jack Markan
6/1/09
Read Re: Natural numbers are uniquely defined
Virgil
6/2/09
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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
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2/5/13
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6/14/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/14/09
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Virgil
6/14/09
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mueckenh@rz.fh-augsburg.de
6/14/09
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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
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Virgil
6/15/09
Read Re: Answer to Dik T. Winter
Virgil
6/16/09
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MeAmI.org
6/16/09
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mueckenh@rz.fh-augsburg.de
6/16/09
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Virgil
6/18/09
Read Re: Answer to Dik T. Winter
mueckenh@rz.fh-augsburg.de
6/18/09
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Virgil
6/20/09
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