```Date: Dec 30, 2012 6:27 PM
Author: Virgil
Subject: Re: Uncountable Diagonal Problem

In article <4036660e-9527-479d-9c47-a1adf9d34d19@px4g2000pbc.googlegroups.com>, "Ross A. Finlayson" <ross.finlayson@gmail.com> wrote:> On Dec 30, 1:33 pm, Virgil <vir...@ligriv.com> wrote:> > In article> > <2fc759b9-3c22-4f0b-83e0-bf9814a3f...@y5g2000pbi.googlegroups.com>,> >  "Ross A. Finlayson" <ross.finlay...@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.> > --> > > Those are definitions, not derived.  Maybe they're "wrong", of the> true nature of the continuum. if false for your "continuum" then that continuum is not the standard real number field.  > > A well ordering of the reals doesn't have uncountably many points in> their natural order.But, if one could find an explicit well-ordering of the reals, it would have to contain all those  uncountably many reals in SOME order.--
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