Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Math Forum
»
Discussions
»
sci.math.*
»
sci.math
Notice: We are no longer accepting new posts, but the forums will continue to be readable.
Topic:
CANTORS PROOF DEMO the Reals are UNCOUNTABLE
Replies:
2
Last Post:
Jan 22, 2013 9:00 PM




AND THIS PROOF CONCLUSION IS TRUE?
Posted:
Jan 10, 2013 8:34 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



