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CANTORS PROOF DEMO the Reals are UNCOUNTABLE
Posted:
Jan 9, 2013 7:34 PM


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 UnCountable!
Herc



