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Topic: Why is it you Guys NEVER ACTUALLY CALCULATE a Real Anti-Diagonal ??
Replies: 15   Last Post: Jan 11, 2013 10:30 PM

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Graham Cooper

Posts: 4,247
Registered: 5/20/10
Re: Why is it you Guys NEVER ACTUALLY CALCULATE a Real Anti-Diagonal ??
Posted: Jan 11, 2013 10:30 PM
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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!





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