Date: Dec 25, 2012 10:23 PM
Author: Virgil
Subject: Re: Simple Refutation of Cantor's Proof

In article 
<aa637598-f327-464f-954b-9cdbe4c875c7@i2g2000pbi.googlegroups.com>,
Graham Cooper <grahamcooper7@gmail.com> wrote:

> > 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.


The one to be constructed is constructed to be of the same length as
the ones listed.
>
> You construct a portion, you construct another portion, and you never
> stop.


One usually creates a rule which defines all the digits of the
construction simultaneously.
>
>
> Take the Transpose Plane
>
> +----->
> | 0. 666..
> | 0. 556..
> | 0. 666..
> | 0. 666..
> | ...
> v
>
> Your 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.
> | ...
> v
>
>
> so your claim is
>
> 0 . T(3,1) T(4,2) T(1,3) ...
>
> is ALSO absent from L(x,y) right?
>
> That's 0.666..
>
> and your claim is
>
> 0 . 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


You have not been listening, then:
The string called the antidiagonal differs in at least
one place from each listed string, so is not listed.
--