Date: Nov 1, 2012 4:03 AM
Author: Hercules ofZeus
Subject: Re: Peer-reviewed arguments against Cantor Diagonalization
On Nov 1, 8:38 am, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> > irrelevant to our purposes here, unless those disputes can explicitly
> > show an invalid step in this very simple proof.)
it DOES NOT HOLD UP TO INDUCTION!!!!!
Examine the lower level Decimal Proof Technique...
ROW1_1=/=AD_1 -> AD=/=ROW1
ROW2_2=/=AD_2 -> AD=/=ROW2
ROW3_3=/=AD_3 -> AD=/=ROW3
AND SO ON!
THIS IS THE INDUCTIVE STEP
P(n) -> P(S(n))
But P(1) DOESNT HOLD BY ITSELF!!!
Proviging a single digit of the diagonal is WORTHLESS, even for ROW 1!
If you claim this is a proof in PREDICATE CALCULUS
then the only Proof Method in PREDICATE CALCULUS
about infinite sets is INDUCTION!
p(1) & p(n)->p(s(n))
-> ALL(n) p(n)
if( if(t(S),f(R)) , if(t(R),f(S)) ).
if the sun's out then it's not raining
if it's raining then the sun's not out