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From: Lawrence D'Oliveiro <ldo@nz.invalid>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Mon, 7 Apr 2025 07:33:05 -0000 (UTC)
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On Sun, 6 Apr 2025 23:38:25 +0100, Richard Heathfield wrote:

> On 06/04/2025 23:01, Lawrence D'Oliveiro wrote:
>
>> On Sun, 6 Apr 2025 07:53:06 +0100, Richard Heathfield wrote:
>> 
>>> After infinitely many steps ...
>> 
>> I.e. never.
> 
> If you mean you can never know all the digits, hey, you're right. 
> No algorithm can derive the number. It's incomputable.

That’s not what “incomputable” means.

> But "never" is a strong word.

Like anything in mathematics, you need proof before claiming something.

This is why we have proof-by-induction: it’s essentially the only way to 
make generalized statements about infinite sequences. Instead of an 
infinite number of propositions to be proved, it boils the whole lot down 
to two:

    P(1)
    P(N) ⊢ P(N + 1)

I gave my proof-by-induction; it is up to you to try to tear it down. If 
you can.