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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 12, 2012 1:20 PM

"LudovicoVan" <julio@diegidio.name> wrote in message
news:k7rehn\$rci\$1@dont-email.me...
> "Zuhair" <zaljohar@gmail.com> wrote in message
>

>> Let a_0 = x_0
>> Let b_0 be the first entry in (x_n) such that b_0 > a_0.
>> Let a_i+1 be the first entry in (x_n) such that a_i < a_i+1 < b_i.
>> Let b_i+1 be the first entry in (x_n) such that a_i+1 < b_i+1 < b_i.

>
> In Cantor's proof a_{i+1} and b_{i+1} are the two first entries
> encountered

That should read: a_{i+1} and b_{i+1} are the first two entries...

-LV

> (in any order) in (x_n) *after* the entries corresponding to a_i and b_i.
> This does not seem to be the case with your proof, where it instead seems
> that entries are just picked every time restarting from the beginning of
> (x_n).
>
> Could you clarify? I'd like to be sure before I proceed reading it...

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