LudovicoVan
Posts:
3,800
From:
London
Registered:
2/8/08


Re: Cantor's first proof in DETAILS
Posted:
Nov 13, 2012 4:44 PM


"Zuhair" <zaljohar@gmail.com> wrote in message news:3929e6b62932401dba0a0a440bb18277@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

