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Topic: Cantor's first proof in DETAILS
Replies: 34   Last Post: Dec 1, 2012 10:56 AM

 Messages: [ Previous | Next ]
 LudovicoVan Posts: 4,165 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
> 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

Date Subject Author
11/12/12 Zaljohar@gmail.com
11/12/12 Zaljohar@gmail.com
11/12/12 Charlie-Boo
11/12/12 Zaljohar@gmail.com
11/13/12 Charlie-Boo
11/15/12 Zaljohar@gmail.com
12/1/12 Frederick Williams
11/12/12 LudovicoVan
11/12/12 LudovicoVan
11/12/12 Uirgil
11/12/12 Shmuel (Seymour J.) Metz
11/12/12 Uirgil
11/13/12 Zaljohar@gmail.com
11/13/12 LudovicoVan
11/13/12 Zaljohar@gmail.com
11/13/12 Zaljohar@gmail.com
11/13/12 Uirgil
11/13/12 LudovicoVan
11/13/12 Uirgil
11/13/12 LudovicoVan
11/13/12 Uirgil
11/13/12 Shmuel (Seymour J.) Metz
11/13/12 Zaljohar@gmail.com
11/13/12 LudovicoVan
11/13/12 Uirgil
11/14/12 Zaljohar@gmail.com
11/14/12 Uirgil
11/14/12 Zaljohar@gmail.com
11/14/12 Zaljohar@gmail.com
11/14/12 Uirgil
11/16/12 LudovicoVan
11/16/12 Uirgil
11/16/12 Zaljohar@gmail.com
11/16/12 LudovicoVan
11/13/12 Shmuel (Seymour J.) Metz