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Topic: Matheology � 258
Replies: 104   Last Post: May 5, 2013 2:26 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 258
Posted: May 5, 2013 4:02 AM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 4 Mai, 22:45, Virgil <vir...@ligriv.com> wrote:
> > In article
> >
> >
> >
> >  WM <mueck...@rz.fh-augsburg.de> wrote:

> > > On 4 Mai, 18:30, Dan <dan.ms.ch...@gmail.com> wrote:
> > > > > > Either they're both relevant to Cantor's argument, or they're both
> > > > > > irrelevant .

> >
> > > > > Cantor's argument
> > IS valid!
> >

> > > > Why should it be considered important under the definition of
> > > > equality? If they have at least one different digit , THEY'RE
> > > > DIFFERENT.

> >
> > > But there always only finitely many with at least one different digit
> > > whereas there are always infinitely many with none different digit.

> >
> > Name one!

>
> A very good question.

So good that WM has no answer to it.
>

>
> > Thus (reals countable) <==> (reals listable).
> >
> > But Cantor has shown that there is no complete list of real possible as
> > every listing of reals necessarily omits some reals.

>
> And counterfactually he has assumed that there is a complete list of
> natural numbers.

If there isn't then the set of naturals is not countable either.
> >
> > > My list is constructed such that all possible squences of digits 1 are
> > > already in the list. No longer sequence is possible

Except for the concatentation of all those listed finite sequences,
which is clearly longer than any of them.

> > Unless your list claims to list all reals, it has no effect on the
> > validity of the Cantor diagonal argument, which remains valid in spite
> > of it.

>
> It is true: If the naturals are complete somewhere, the reals cannot
> be complete there. Alas this theorem is void since the naturals cannot
> be complete anywhere.

Then the set of naturals is also not a countable set.

At least not in Wolkenmuekenheim.

But outside Wolkenmuekenheim, the set of naturals IS countable and the
set of reals is NOT.
--

Date Subject Author
4/29/13 Virgil
4/29/13 mueckenh@rz.fh-augsburg.de
4/29/13 Virgil
4/30/13 dan.ms.chaos@gmail.com
4/30/13 mueckenh@rz.fh-augsburg.de
4/30/13 dan.ms.chaos@gmail.com
4/30/13 mueckenh@rz.fh-augsburg.de
4/30/13 Virgil
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 Virgil
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 Virgil
5/1/13 dan.ms.chaos@gmail.com
5/1/13 JT
5/2/13 mueckenh@rz.fh-augsburg.de
5/2/13 Ed Prochak
5/2/13 Virgil
5/2/13 mueckenh@rz.fh-augsburg.de
5/2/13 dan.ms.chaos@gmail.com
5/2/13 mueckenh@rz.fh-augsburg.de
5/2/13 Virgil
5/3/13 dan.ms.chaos@gmail.com
5/3/13 mueckenh@rz.fh-augsburg.de
5/3/13 dan.ms.chaos@gmail.com
5/3/13 Virgil
5/3/13 mueckenh@rz.fh-augsburg.de
5/3/13 dan.ms.chaos@gmail.com
5/3/13 mueckenh@rz.fh-augsburg.de
5/3/13 dan.ms.chaos@gmail.com
5/3/13 mueckenh@rz.fh-augsburg.de
5/3/13 dan.ms.chaos@gmail.com
5/4/13 mueckenh@rz.fh-augsburg.de
5/4/13 dan.ms.chaos@gmail.com
5/4/13 mueckenh@rz.fh-augsburg.de
5/4/13 dan.ms.chaos@gmail.com
5/4/13 mueckenh@rz.fh-augsburg.de
5/4/13 dan.ms.chaos@gmail.com
5/4/13 mueckenh@rz.fh-augsburg.de
5/4/13 dan.ms.chaos@gmail.com
5/4/13 mueckenh@rz.fh-augsburg.de
5/4/13 dan.ms.chaos@gmail.com
5/4/13 ross.finlayson@gmail.com
5/5/13 LudovicoVan
5/5/13 fom
5/5/13 ross.finlayson@gmail.com
5/5/13 ross.finlayson@gmail.com
5/5/13 mueckenh@rz.fh-augsburg.de
5/5/13 Virgil
5/5/13 dan.ms.chaos@gmail.com
5/5/13 mueckenh@rz.fh-augsburg.de
5/4/13 Virgil
5/5/13 mueckenh@rz.fh-augsburg.de
5/5/13 Virgil
5/4/13 Virgil
5/4/13 Virgil
5/5/13 mueckenh@rz.fh-augsburg.de
5/5/13 Virgil
5/5/13 mueckenh@rz.fh-augsburg.de
5/4/13 fom
5/4/13 Virgil
5/4/13 ross.finlayson@gmail.com
5/4/13 Virgil
5/4/13 Virgil
5/4/13 Virgil
5/4/13 trj
5/4/13 Virgil
5/3/13 Virgil
5/3/13 Virgil
5/3/13 fom
5/3/13 dan.ms.chaos@gmail.com
5/3/13 fom
5/3/13 gus gassmann
5/3/13 Virgil
5/2/13 Virgil
5/1/13 Virgil
5/1/13 JT
5/1/13 Virgil
5/1/13 JT
5/1/13 Bergholt Stuttley Johnson
5/1/13 rt servo
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 Virgil
5/1/13 Virgil
5/1/13 Virgil
5/1/13 Virgil
5/1/13 Virgil
4/30/13 Virgil
4/30/13 mueckenh@rz.fh-augsburg.de
4/30/13 Virgil
4/29/13 ross.finlayson@gmail.com
4/29/13 Virgil