Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Matheology § 264 Hilbert's Hotel: checking out.
Replies: 16   Last Post: May 13, 2013 3:29 AM

 Messages: [ Previous | Next ]
 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology § 264 Hilbert's Hotel: checking out.
Posted: May 12, 2013 3:30 AM

On 11 Mai, 21:46, Virgil <vir...@ligriv.com> wrote:
> In article
>
>  WM <mueck...@rz.fh-augsburg.de> wrote:

> > First enumerate the first two rationals q_2 = 1/2 and q_1 = 1/3. Then
> > take off label 1 from 1/3 and enumerate the first irrational x_1 and
> > attach label 2 to the first rational 1/2. 1/3 will get remunerated and
> > re-enumerated in the next round by label label 3, when 1/2 will leave
> > its 2 but gain label 4 instead. So 1/2 and 1/3 will become q_4 and
> > q_3.

>
> > Continue until you will have enumerated the first n rationals and the
> > first n irrationals

>
> > q_2n, q_2n-1, ..., q_n+1   and   x_n, x_n-1, ..., x_1
>
> > and if you got it by now, then go on until you will have enumerated
> > all of them.

>
>  What deludes WM into supposing that either this, or any other method,
> will ever have ennumerated ALL irrationals?

The algebraic irrationals shoudl all be enumerated. None should have
escaped.
>
> > Then you have proved in ZFC that there are no rational
> > numbers.

>
> Not outside of Wolkenmuekenheim. because only the corruptions in
> WMytheology allow him to presume any ennumeration of all irrationals.

I did not say so. Your argument aims at a strawman.

Regards, WM

Date Subject Author
5/11/13 mueckenh@rz.fh-augsburg.de
5/11/13 Bergholt Stuttley Johnson
5/11/13 Virgil
5/12/13 mueckenh@rz.fh-augsburg.de
5/12/13 Virgil
5/12/13 mueckenh@rz.fh-augsburg.de
5/12/13 Virgil
5/12/13 gus gassmann
5/12/13 Virgil
5/12/13 gus gassmann
5/12/13 Virgil
5/13/13 yashvendars@gmail.com
5/13/13 Virgil