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

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Uirgil

Posts: 183
Registered: 4/18/12
Re: Cantor's first proof in DETAILS
Posted: Nov 12, 2012 5:05 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article <k7rehn$rci$1@dont-email.me>,
"LudovicoVan" <julio@diegidio.name> wrote:

> "Zuhair" <zaljohar@gmail.com> wrote in message
> news:86a85cce-2a84-4c9f-b860-527958274b50@o8g2000yqh.googlegroups.com...
>

> > 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
> (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).


It does not seem that way to those who are capable of reading what
Zuhair said.
>
> Could you clarify? I'd like to be sure before I proceed reading it...


What is not clear? Zuhair's plan clearly produces a nested sequence of
closed intervals I_i = [a_i,b_i] with each I_(n+1) a proper subinterval
of the interior of I_n.


Date Subject Author
11/12/12
Read Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/12/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/12/12
Read Re: Cantor's first proof in DETAILS
Charlie-Boo
11/12/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/13/12
Read Re: Cantor's first proof in DETAILS
Charlie-Boo
11/15/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
12/1/12
Read Re: Cantor's first proof in DETAILS
Frederick Williams
11/12/12
Read Re: Cantor's first proof in DETAILS
LudovicoVan
11/12/12
Read Re: Cantor's first proof in DETAILS
LudovicoVan
11/12/12
Read Re: Cantor's first proof in DETAILS
Uirgil
11/12/12
Read Re: Cantor's first proof in DETAILS
Shmuel (Seymour J.) Metz
11/12/12
Read Re: Cantor's first proof in DETAILS
Uirgil
11/13/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/13/12
Read Re: Cantor's first proof in DETAILS
LudovicoVan
11/13/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/13/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/13/12
Read Re: Cantor's first proof in DETAILS
Uirgil
11/13/12
Read Re: Cantor's first proof in DETAILS
LudovicoVan
11/13/12
Read Re: Cantor's first proof in DETAILS
Uirgil
11/13/12
Read Re: Cantor's first proof in DETAILS
LudovicoVan
11/13/12
Read Re: Cantor's first proof in DETAILS
Uirgil
11/13/12
Read Re: Cantor's first proof in DETAILS
Shmuel (Seymour J.) Metz
11/13/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/13/12
Read Re: Cantor's first proof in DETAILS
LudovicoVan
11/13/12
Read Re: Cantor's first proof in DETAILS
Uirgil
11/14/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/14/12
Read Re: Cantor's first proof in DETAILS
Uirgil
11/14/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/14/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/14/12
Read Re: Cantor's first proof in DETAILS
Uirgil
11/16/12
Read Re: Cantor's first proof in DETAILS
LudovicoVan
11/16/12
Read Re: Cantor's first proof in DETAILS
Uirgil
11/16/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/16/12
Read Re: Cantor's first proof in DETAILS
LudovicoVan
11/13/12
Read Re: Cantor's first proof in DETAILS
Shmuel (Seymour J.) Metz

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