Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: Lawrence D'Oliveiro <ldo@nz.invalid>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Fri, 4 Apr 2025 08:05:08 -0000 (UTC)
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On Fri, 4 Apr 2025 08:41:35 +0100, Richard Heathfield wrote:

> On 04/04/2025 08:21, Lawrence D'Oliveiro wrote:
>>
>> 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.
> 
> Show me your first N digits, and I'll show you a counterexample.

Counterexample to what?

>> Therefore there is guaranteed to be some number we haven’t looked at
>> yet with all those first N digits the same.
> 
> And yet you still won't post those first N digits.

Digit 1 is the first digit of entry 1 in the list.
Digit 2 is the second digit of entry 2 in the list.
..
..
..
Digit N is the Nth digit of entry N in the list.