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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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Graham Cooper

Posts: 4,280
Registered: 5/20/10
AND THIS PROOF CONCLUSION IS TRUE?
Posted: Jan 10, 2013 8:34 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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