```Date: Dec 25, 2012 6:00 PM
Author: Virgil
Subject: Re: Simple Refutation of Cantor's Proof

In article <67261d2b-d57e-4174-af7b-921ac287e30d@r4g2000pbi.googlegroups.com>, Graham Cooper <grahamcooper7@gmail.com> wrote:> On Dec 25, 7:22 pm, Virgil <vir...@ligriv.com> wrote:> > > > > [1] you change each digit ONE AT A TIME> > > > > 0.694...> > > > > but this process NEVER STOPS> >> > > > > [2] and you NEVER CONSTRUCT A NEW DIGIT SEQUENCE!> >> > > > Do you deny that f(x) = x^2 and g(x) = 2*x+3 define real functions,> > > > i.e., functions taking arbirary real numbers as arguments and producing> > > > from them appropriate real numbers as values?> >> > > > It you accept them as functions why balk at functions from |N to> > > > the set of decimal digits, interpreted as reals in [0,1]?> >> > > the logical manipulations do not hold on AD(x) = D(x)+1   [mod 9]> >> > > This is what you are really doing.> >> > > +----->> > > | 0. 542..> > > | 0. 983..> > > | 0. 143..> > > | 0. 543..> > > | ...> > > v> >> > > T(x,y) = L(x,y)+1   [mod 9]> >> > > +----->> > > | 0. 653..> > > | 0. 004..> > > | 0. 254..> > > | 0. 654..> > > | ...> > > v> >> > > This plane exists as much as your altered string.> >> > > It's mere naivety to define any digit string from> >> > > 0 . T(1,_)  T(2,_)  T(3,_) ...> >> > > where the set of free values _ biject N> > > and then conclude such strings are absent from L.> >> > > Herc> >> > Since that is not a rule used by anyone who knows what is needed, it is> > irrelevant,> >> > A rule that actually works on decimals, or with any base larger than 7,> > is to look at the nth digit of the nth element in the list and if it> > less than a 6 make the nth digit of the "anti-diagonal a  6 but> > otherwise make it a 5.> >> > OK!> > +----->> | 0. 542..> | 0. 983..> | 0. 143..> | 0. 543..> | ...> v> > T(x,y) = 6  IFF L(x,y) < 6> T(x,y) = 5 OTHERWISE> > > +----->> | 0. 666..> | 0. 556..> | 0. 666..> | 0. 666..> | ...> v> > This plane exists as much as your altered string.> It's mere naivety to define any digit string from> > 0 . T(1,_)  T(2,_)  T(3,_) ...> > where the set of free values _ biject N> and then conclude such strings are absent from L.> > HercSince the constructed string must differ from each string listed in L in a way that gives it a different value from that listed string, how can it possibly still be among a set of values from which it is by construction excluded?--
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