```Date: Dec 25, 2012 3:56 AM
Author: Graham Cooper
Subject: Re: Simple Refutation of Cantor's Proof

On Dec 25, 3:05 pm, Virgil <vir...@ligriv.com> wrote:> In article> <8526068c-c873-4164-88f9-8717127e3...@ah9g2000pbd.googlegroups.com>,>  Graham Cooper <grahamcoop...@gmail.com> wrote:>>>>>>>>>> > On Dec 25, 4:48 am, William Hughes <wpihug...@gmail.com> wrote:> > > On Dec 24, 4:01 am, Graham Cooper <grahamcoop...@gmail.com> wrote:>> > > > +----->> > > > | 0. 542..> > > > | 0. 983..> > > > | 0. 143..> > > > | 0. 543..> > > > | ...> > > > v>> > > > OK - THINK>> > > Induction>> > only in the HR sense Will!>> > OK some great replies here!>> > I think WM point is correct here, the ENTIRE LIST can exist>> > +----->> > | 0. 542..> > | 0. 983..> > | 0. 143..> > | 0. 543..> > | ...> > v>> > each digit a FINITE distance from the Origin.>> > There is no constructible issue with the List itself.>> > ---------------------->> > And GG has a good point, once he saw my 2 claims Sequitur together>> > [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..| ...vT(x,y) = L(x,y)+1   [mod 9]+----->| 0. 653..| 0. 004..| 0. 254..| 0. 654..| ...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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