Virgil
Posts:
4,661
Registered:
1/6/11
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Re: Uncountable Diagonal Problem
Posted:
Jan 1, 2013 7:05 PM
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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.
--
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