Date: Nov 12, 2012 5:05 PM
Author: Uirgil
Subject: Re: Cantor's first proof in DETAILS

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.