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..

| ...

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