Date: Jan 11, 2013 10:30 PM
Author: Graham Cooper
Subject: Re: Why is it you Guys NEVER ACTUALLY CALCULATE a Real Anti-Diagonal ??
On Jan 12, 1:13 pm, Daryl McCullough <stevendaryl3...@yahoo.com>

wrote:

> Cantor's proof says that for any infinite sequence of reals, there is another

> real that is not on that list. You didn't give an infinite sequence of reals,

> so there is really nothing to refute. But for definiteness, the real

>

> 0.101001000100001000001...

>

> is not on your list.

*********THIS IS/WAS YOUR PROOF********

A SUBLIST OF REALS IN [BASE 4]

R1 0.0000...

R2 0.3333...

R3 0.3210...

...

DIAGONAL = 0.031...

DEFINE

AD(d) = 2 IFF DIAGONAL(d) < 2

AD(d) = 1 IFF DIAGONAL(d) > 1

AD=0.212... is MISSING FROM THE LIST

PROOF

DIGIT 1 (2) IS DIFFERENT TO LIST[1,1] (0)

DIGIT 2 (1) IS DIFFERENT TO LIST[2,2] (3)

DIGIT 3 (2) IS DIFFERENT TO LIST[3,3] (1)

AND SO ON

So AD is DIFFERENT to EVERY ROW

since This Holds For Any Arbitrary List Of Reals

there is a missing Real for any List Of Reals

therefore Reals are Un-Countable!