LudovicoVan
Posts:
2,971
From:
London
Registered:
2/8/08
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Re: Cantor's first proof in DETAILS
Posted:
Nov 13, 2012 4:44 PM
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"Zuhair" <zaljohar@gmail.com> wrote in message
news:3929e6b6-2932-401d-ba0a-0a440bb18277@y6g2000vbb.googlegroups.com...
> On Nov 13, 11:16 pm, Uirgil <uir...@uirgil.ur> wrote:
<snip>
>> Your alleged argument against the Cantor proof does not work against
>> either Cantor's proof, nor Zuhair's proof, nor my proof for that matter,
>> since your N* is irrelevant for all of them.
>
> I showed in the Corollary that even if he use N* as the domain of
> (x_n), still we can prove there is a missing real from the range of
> (x_n). So Cantor's argument or my rephrasing of it both can easily be
> shown to be applicable to N* (any set having a bijection with N) as
> well as N.
You are simply missing the point there: we don't need N* to disprove Cantor,
we need N* to go beyond it and the standard notion of countability. In
fact, that there is a bijection between N* and N is a bogus argument too, as
the matter is rather about different order types.
-LV
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