Date: Jan 1, 2013 7:05 PM
Author: Virgil
Subject: Re: Uncountable Diagonal Problem
In article

<d0cf5fff-92d8-4229-aec3-499754ae6cf0@r10g2000pbd.googlegroups.com>,

"Ross A. Finlayson" <ross.finlayson@gmail.com> wrote:

> On Jan 1, 2:57 pm, Virgil <vir...@ligriv.com> wrote:

> > In article

> > <659c05ff-5b34-4ebe-9617-4d54292a9...@pp8g2000pbb.googlegroups.com>,

> > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:

> >

> > > The transfinite course-of-passage in well-ordering the reals sees

> > > a diminishing interval. Do the endpoints of the interval meet,

> > > in the well-ordering? A critical point of Cantor's first is that

> > > the intersection is non-empty.

> >

> > It is a well known property of the real number line, at least among

> > Mathematicians, that a nested sequence of closed intervals has

> > non-empty Intersection.

> >

> > Does Ross claim otherwise? --

>

> http://www.tiki-lounge.com/~raf/finlayson_injectrationals.pdf

That paper, even if it were valid, would not invalidate that a nested

sequence of closed intervals in R necessarily has non-empty intersection.

--