|
|
Re: Matheology § 210
Posted:
Feb 6, 2013 9:43 AM
|
|
On 6 Feb., 00:31, Virgil <vir...@ligriv.com> wrote:
> In article
> <3ffb012f-81a5-410d-8257-f8eee410a...@e10g2000vbv.googlegroups.com>,
>
> WM <mueck...@rz.fh-augsburg.de> wrote:
> > But how to pick this dark matter of numbers? Only accessible numbers
> > can get picked. Unpickable numbers cannot appear anywhere, neither in
> > mathematics nor in Cantor's lists. Therefore Cantor "proves" that the
> > pickable numbers, for instance numbers that can appear as an
> > antidiagonal of a defined list, i.e., the countable numbers, are
> > uncountable.
>
> Nonsense!
>
> What Cantor proved was that no list of accessible real numbers
> (accessible because listable) can include all accessible numbers,
> because any such list itself proves the existence of numbers not listed.
Correct. And König proved (or at least knew the fact) that the set of
accessible numbers is countable.
Regards, WM
|
|
