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Re: Matheology § 238
Posted:
Apr 13, 2013 4:52 AM
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On 13 Apr., 02:31, Virgil <vir...@ligriv.com> wrote:
> In article
> <db84da07-1059-47c3-a396-bb918dc92...@c15g2000vbl.googlegroups.com>,
>
> WM <mueck...@rz.fh-augsburg.de> wrote:
> > Cantor shows that by the diagonal argument the n-th line can be
> > removed from the set of potential duplicates of d.
> > He concludes that every line can be removed from the set of
> > potential duplicates of d.
>
> WM may claim that, but Cantor never said anything like it.
>
> What Cantor DID say was that given any list of infinite binary sequences
> of letters from {"m","w"}, there is at least one such sequence not
> listed
and he did not only claim (like you), but he proved this statement by
continuing: da sonst für das betreffende m und für alle ganzzahligen
Werte von n
b_n = a_m,n
also auch im besonderen
b_m = a_mm.
This shows that for every m : a_m can be removed from the set of
potential candidates for the identity b = a_m.
Yes, that is what he did. And I guess that during his whole life he
never, not even remotely, considered the possibility that
A) every a_m can be removed from the list of candidates
could fail to imply
C) All a_m can be removed from the list of candidates,
such that this list is empty after removing has been completed.
Regards, WM
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