fom
Posts:
1,969
Registered:
12/4/12
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Re: Matheology § 238
Posted:
Apr 13, 2013 5:04 AM
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On 4/13/2013 3:52 AM, WM wrote:
> 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.
Well, since he was effectively paying for the sins
of Isaac Newton, arguing for the end of established
physics would have been just about the last thing
he would have "remotely" considered.
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