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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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