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From: Lawrence D'Oliveiro <ldo@nz.invalid>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Sat, 5 Apr 2025 07:38:19 -0000 (UTC)
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On Fri, 4 Apr 2025 09:16:17 +0100, Richard Heathfield wrote:

> Since all elements (except your two openers) begin with a 3, none of
> them start 12, and so after just two iterations we have already
> constructed a number that's not in the infinite list.

Remember that the hypothesis of the Cantor “proof” is that the list is 
already supposed to contain every computable number. The fact that the 
contruction succeeds for your list examples does not mean it will succeed 
with mine. Remember, the “proof” depends on it succeeding in the general 
case, with every possible list.