```Date: Dec 25, 2012 12:05 AM
Author: Virgil
Subject: Re: Simple Refutation of Cantor's Proof

In article <8526068c-c873-4164-88f9-8717127e3bfa@ah9g2000pbd.googlegroups.com>, Graham Cooper <grahamcooper7@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]? > > ----------------------> > this is actually 100% correct under Static and Process analysis.> > ----------------------> > GG counter example of> > f(x) = 2*x> > HOLDING for the infinite domain> is a good point however, although> he had to hand pick the example so> it doesn't contradict> > [1]> [1]->[2]> [2]> > You never construct a new digit Sequence> QED> > > Merry Xmas!> > Herc> --> www.CAMGIRLS.com> TOTAL: \$2834  2012-12-21 Fri> Not the End of the World!--
```