Article View: sci.logic
Article #745Re: Diagonalization with pages
From: Tonico
Date: Wed, 18 Jan 2012 11:42
Date: Wed, 18 Jan 2012 11:42
52 lines
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3347 bytes
On Jan 18, 5:37 am, Graham Cooper <grahamcoop...@gmail.com> wrote: > On Jan 18, 12:53 pm, Tim Little <t...@little-possums.net> wrote: > > > On 2012-01-17, Gustavo Broos <gpu...@gmail.com> wrote: > > > > But how do we prove that the power set is uncountable: again by > > > using Cantor's theorem or the diagonal argument. So we continue in > > > the loop without proving what we want to prove. > > > Continue in what loop? The diagonal argument is finite and valid. > > It does not require any "loops". > > Yes it does! > > MISSING(S, e) <=> ALL(n) S(n)=/=e <<DEFN > > MISSING(LIST, ANTIDIAG(LIST)) <<CLAIM > > => ALL(n) LIST(n)=/=ANTIDIAG(LIST) <<Required To Prove > > ASSUME > ALL(d) ANTIDIAG(LIST)_d =/= LIST(d)_d > > -> > ALL(d) > LIST(d)=/=ANTIDIAG(LIST) > > You ASSUME a extra_parameterised version of the formula you are trying > to prove. > > > > > The only loop appears to be in your repeated postings of complete > > misunderstandings and mischaracterizations of that argument. > > > -- > > Tim > > In context, the argument was: > > PAGE 1 = ARBITRARY LIST > > PAGE 2 = ANTIDIAGONAL OF ALL INF_MANY PERMUTATIONS OF PAGE 1 > > How do you prove INF_MANY PERMUTATIONS OF PAGE 1 > > is uncountable without using the Powerset Proof? > > Herc Idiot
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From: Tonico <Tonicopm@yahoo.com>
Newsgroups: sci.logic,sci.physics,aus.science
Subject: Re: Diagonalization with pages
Date: Wed, 18 Jan 2012 03:42:10 -0800 (PST)
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