```Date: Dec 25, 2012 7:29 PM
Author: Graham Cooper
Subject: Re: Simple Refutation of Cantor's Proof

On Dec 26, 9:00 am, Virgil <vir...@ligriv.com> wrote:> In article> <67261d2b-d57e-4174-af7b-921ac287e...@r4g2000pbi.googlegroups.com>,>  Graham Cooper <grahamcoop...@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.>> > Herc>> Since 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?>the size of the string is not fixed.You construct a portion, you construct another portion, and you neverstop.Take the Transpose Plane +-----> | 0. 666.. | 0. 556.. | 0. 666.. | 0. 666.. | ... vYour construction is now the DIAGONAL of that plane.0 . T(1,1)  T(2,2)  T(3,3) ... +-----> | 0. 6  .. | 0.  5 .. | 0.   6.. | 0. | ... vso your claim is0 . T(3,1) T(4,2) T(1,3) ...is ALSO absent from L(x,y) right?That's  0.666..and your claim is0 . T(2,1) T(4,2) T(1,3) ...is ALSO absent from L(x,y)That's 0.566..So every digit you add to the missing string is arbitrary.Herc
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