```Date: Dec 25, 2012 4:01 PM
Author: Graham Cooper
Subject: Re: Simple Refutation of Cantor's Proof

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..| ...vT(x,y) = 6  IFF L(x,y) < 6T(x,y) = 5 OTHERWISE+----->| 0. 666..| 0. 556..| 0. 666..| 0. 666..| ...vThis plane exists as much as your altered string.It's mere naivety to define any digit string from0 . T(1,_)  T(2,_)  T(3,_) ...where the set of free values _ biject Nand then conclude such strings are absent from L.Herc
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