Date: Jan 9, 2013 7:34 PM
Author: Graham Cooper
Subject: CANTORS PROOF DEMO the Reals are UN-COUNTABLE
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!

Herc