Date: Nov 13, 2012 4:44 PM
Author: LudovicoVan
Subject: Re: Cantor's first proof in DETAILS
"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