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Article #461

Re: Church's Heresy and the Unsolveability of chess

#461
From: Mark
Date: Tue, 06 Oct 1992 20:23
18 lines
1375 bytes
I expound on The Church's Heresy:
>   The strong version of Church's Heresy: the set of all functions that have
>been, are being, ever will be, or ever could be computed is a finite subset
>of the recursive functions bounded above in size by 2-to-the-256.

>Corollary: Every computable function can be represented uniquely by 32 bytes.
>Theorem:   This 32-byte coding is not computable, but is finite and recursive.

In article <1992Oct6.112819.16016@odin.diku.dk> torbenm@diku.dk (Torben AEgidius Mogensen) writes:
>No. It is only the size of the functions that can be represented in 32
>bytes. The functions themselves needs 2^256 bytes.

There are 2^256 32 byte integers.  Therefore there is a one-to-one
correspondence between 32 byte integers and computeable functions (which
there are less than 2^256 of).

Furthermore, this mapping is finite, therefore it is a recursive function.
It's just not computeable.
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Path: arc1-ca.pugleaf.net!sparky!uunet!caen!uwm.edu!csd4.csd.uwm.edu!markh
From: markh@csd4.csd.uwm.edu (Mark)
Newsgroups: sci.logic
Subject: Re: Church's Heresy and the Unsolveability of chess
Date: 6 Oct 1992 20:23:34 GMT
Organization: Computing Services Division, University of Wisconsin - Milwaukee
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