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
>  Graham Cooper <grahamcoop...@gmail.com> wrote:
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> > On Dec 25, 4:48 am, William Hughes <wpihug...@gmail.com> wrote:
> > > On Dec 24, 4:01 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
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> > > > +----->
> > > > | 0. 542..
> > > > | 0. 983..
> > > > | 0. 143..
> > > > | 0. 543..
> > > > | ...
> > > > v

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> > > > OK - THINK
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> > > Induction
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> > only in the HR sense Will!
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> > OK some great replies here!
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> > I think WM point is correct here, the ENTIRE LIST can exist
>
> > +----->
> > | 0. 542..
> > | 0. 983..
> > | 0. 143..
> > | 0. 543..
> > | ...
> > v

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> > each digit a FINITE distance from the Origin.
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> > There is no constructible issue with the List itself.
>
> > ----------------------
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> > 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