Re: Diagonalization with pages

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Article #756

#756

From: Tonico
Date: Sun, 15 Jan 2012 11:10

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On Jan 15, 11:39 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Jan 15, 4:46 am, Gustavo Broos <gpu...@gmail.com> wrote:
>
> > The idea is to generate infinite new binary strings from the original
> > list of strings by using not only the usual diagonal, but any other
> > permutation on the columns (there would be an infinite number of
> > permutations).
>
> Exactly!  This is entirely computable too.
>
> The standard Cantor's Proof is Given ONE List of Reals.
>
> Given an infinite set of lists there is always a
> DIAGONAL(LIST-p) = ANTIDIAGONAL(LIST-n)
>
> where LIST-p and LIST-n are the same set of reals, it's just different
> permutations that determine the phantom diagonals.
>
> In Cantor's proof, given LIST-p, p is a free variable that is never
> bound in their proof.
>
> The computable approach to your method is to use an infinite sequence
> of Universal Turing Machines to compute infinitely many lists of
> reals.
>
> UTMa = <tm1, tm2, tm3, tm4, tm5, ....>
>
> An infinite subset of those tm's are UTMS themselves!
>
> UTMa = <utm1, utm2, utm3, utm4, utm5, ...>
>
> Each utm computes a usually-new permutation of the same set of
> computable reals.
>
> Uncomputable Reals like OMEGA also disappear in this model!
>
> Herc


Idiot

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From: Tonico <Tonicopm@yahoo.com>
Newsgroups: sci.logic,sci.physics,rec.org.mensa,aus.science
Subject: Re: Diagonalization with pages
Date: Sun, 15 Jan 2012 03:10:34 -0800 (PST)
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