Re: Error in Turing's paper 'On computable numbers, with an application to th..

From: KRamsay (kramsay_at_aol.com)
Date: 08/23/04 

Date: 23 Aug 2004 09:27:53 GMT

In article <gT6Wc.30535$9Y6.22391@newsread1.news.pas.earthlink.net>, "r.e.s."
<r.s@ZZmindspring.com> writes:
|Wouldn't you agree that Specker's example (referenced in
|my earlier posting) is simpler than one involving a
|Chaitin's Omega?
|
|Just take any non-recursive r.e. subset of N, say A, and
|consider a computable enumeration of subsets of A such
|that 0 \subset A_1 \subset A_2 \subset A_3 ..., whose
|union is A. Now define x_n to be the real number whose
|binary expansion has 1 in the kth place iff k is in A_n.

Sure, just a little simpler. I thought about switching to the
real whose n-th bit is 1 if the n-th Turing machine halts when
started on a blank tape, but didn't bother.

Keith Ramsay

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