Uirgil
Posts:
185
Registered:
4/18/12


Re: Cantor's first proof in DETAILS
Posted:
Nov 12, 2012 5:05 PM


In article <k7rehn$rci$1@dontemail.me>, "LudovicoVan" <julio@diegidio.name> wrote:
> "Zuhair" <zaljohar@gmail.com> wrote in message > news:86a85cce2a844c9fb860527958274b50@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.

