```Date: Jan 1, 2013 6:20 PM
Author: Graham Cooper
Subject: Re: Uncountable Diagonal Problem

On Dec 31 2012, 9:27 am, Virgil <vir...@ligriv.com> wrote:> In article> <4036660e-9527-479d-9c47-a1adf9d34...@px4g2000pbc.googlegroups.com>,>  "Ross A. Finlayson" <ross.finlay...@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.>LETS TRY!LISTR1   0.11111111...R2   0.22222222...R3   0.01010101...R4   0.99999999......DIAGONAL =  0.1209....WHAT ARE ALL THE MISSING REALS VIRGIL?HINT:  you should be able to calculate 9*9*9*9 of them?JUST FROM THAT LIST!WOW!  THERE REALLY ARE A LOT OF UNCOUNTABLE REALS!!Herc
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