EUREKA Cantor exposed.... sci.math curls tails between legs..

From: |-|erc (h_at_r.c)
Date: 12/10/04 

Date: Fri, 10 Dec 2004 17:41:00 +1000

Assume a real number list L where
L(a) is the ath real
L(a, b) is the bth digit of the ath real.

Required To Prove :
the list is incomplete
=
Er e R, Aa e N, L(a) =/= r
=
Er e R, Aa e N, Eb e N, L(a, b) =/= r(b) ...r(b) is the bth digit of r

Assume r is on the list
Ea e N, L(a) = r [1]
=
Ea e N, Ab e N, L(a, b) = r(b)

Let
r(b) = L(b,b)+1 (mod 9) [2]
=>
r(b) = !L(b,b) ...! is some digit change function

Therefore
Ea e N, Ab e N, L(a,b) = !L(b,b)

When a=b
Ea e N, L(a,a) =!L(a,a)
=>
Ec e N, c=!c
CONTRADICTION

CONCLUSION
NOT (Ea e N, L(a) = r AND r(b) = L(b,b)+1) ...[1] AND [2]
=
NOT (Ea e N, Ab e N, L(a, b) = L(b, b) + 1)
=
NOT (Ea e N, Ab e N, L(a, b) != L(b, b))
=
Aa e N, Eb e N, L(a, b) = L(b, b)

AXIOM
all reals in the list have a digit on the diagonal that equals itself

Herc 

--
> then it is uniquely defined AFTER the flippers have flipped
> enough (given that every flipper is only a finite number of
> flippers from the beginning, and every flip is only a finite
> number of flips from the beginning, no individual flip or anti-
> flip needs infinite inputs to compute).   GEORGE GREENE sci.logic

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