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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Thu, 10 Apr 2025 10:51:22 +0300
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On 2025-04-10 00:52:14 +0000, Lawrence D'Oliveiro said:

> On Mon, 7 Apr 2025 11:40:58 +0300, Mikko wrote:
> 
>> Even there, proving that a computable list of all computable numbers
>> does not exist.
> 
> But the ability to construct an infinite list of reals or computables is a
> basic assumption of the Cantor construction. If you’re saying it’s not
> possible to construct such a list, then that’s the end of Cantor’s proof.

No, it is not. Of course, if there is no such list it immediately follows
that there is not such list, so only the possibility that there is such
list requires further consderation. There is no requirement that any such
list (if there are any) is constructible. The proof is about every list,
whether constructible or not.

-- 
Mikko