Date: Dec 30, 2012 4:33 PM
Author: Virgil
Subject: Re: Uncountable Diagonal Problem

In article 
<2fc759b9-3c22-4f0b-83e0-bf9814a3fdae@y5g2000pbi.googlegroups.com>,
"Ross A. Finlayson" <ross.finlayson@gmail.com> wrote:

> Formulate Cantor's nested intervals with "mega-sequences" (or
> transfinite sequence or ordinal-indexed sequence) instead of sequences
> of endpoints. Well-order the reals and apply, that the sequences
> converge yet have not emptiness between them else there would be two
> contiguous points, in the linear continuum.


Not possible with the standard reals without violating such properties
of the reals as the LUB and GLB properties:
Every non-empty set of reals bounded above has a real number LUB.
Every non-empty set of reals bounded below has a real number GLB.
--