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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 4, 2013 4:45 PM

In article
WM <mueckenh@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!
>
> > Every finite digit appears in the list at least once , but NEVER DO
> > ALL OF THEM APPEAR AT ONCE , IN THE SAME NUMBER.

>
> Stop shouting.

Since nothing less seems able to penetrate the crenelated battlements of
Schloss Wolkenmuekenheim, why not?
>
> >
> > THIS IS REQUIRED TO DISPROVE CANTOR :
> > exists n , forall m ,  a_nm = d_m

>
> Of course, in a list that contains all rationals, this is easily
> proved.
> A simpler case is the list:
>
> 0.0
> 0.1
> 0.11
> 0.111
> ...

With 0,0111... as its anti-dialgonal, so WM loses again.

> Your assertion that in your anti-diagonal there are more than all
> digits that are already covered by the list is simply nonsense.

Since no one made any such argument, except WM, it is WM's nonsense.

The standard mathematical definition of a set, S, being countable is
that there is some mapping from |N to S that is surjective, i.e., such
that every member of S is the image of some member of |N.

Such a mapping constitutes a 'listing' of the members of S with the
members position(s) in the list being the appropriate member(s) of |N.

Thus for WM, or anyone else, to successfully claim that the set of reals
is countable is equivalent to claiming that the set of real is listable.

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.

>
>
> My list is constructed such that all possible squences of digits 1 are
> already in the list. No longer sequence is possible (otherwise it
> would be in the list) and a shorter sequence cannot support Cantor's
> claim.

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.
>
--

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