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Topic:
CANTORS PROOF DEMO the Reals are UN-COUNTABLE
Replies:
2
Last Post:
Jan 22, 2013 9:00 PM
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CANTORS PROOF DEMO the Reals are UN-COUNTABLE
Posted:
Jan 9, 2013 7:34 PM
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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
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