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From: Lawrence D'Oliveiro <ldo@nz.invalid>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Fri, 4 Apr 2025 07:21:36 -0000 (UTC)
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On Fri, 4 Apr 2025 07:24:35 +0100, Richard Heathfield wrote:

> On 04/04/2025 07:15, Lawrence D'Oliveiro wrote:
>
>> On Fri, 4 Apr 2025 06:16:20 +0100, Richard Heathfield wrote:
>> 
>>> The Cantor diagonal argument shows that *any* list, finite or
>>> infinite,
>>> is incomplete.
>> 
>> But it takes an infinite number of steps to show that for an infinite
>> list. And at every point, the probability that the N digits computed so
>> far match some number later in the list is 1.
> 
> Depends on the list.

No it doesn’t. At every point N, we have the first N digits of our 
hypothetical number-that-is-not-in-the-list. But we have an infinitude of 
remaining numbers in the list we haven’t looked at, among which all 
possible combinations of those N digits will occur. Therefore there is 
guaranteed to be some number we haven’t looked at yet with all those first 
N digits the same.