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From: Richard Heathfield <rjh@cpax.org.uk>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Fri, 4 Apr 2025 08:41:35 +0100
Organization: Fix this later
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On 04/04/2025 08:21, Lawrence D'Oliveiro wrote:
> 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.

Show me your first N digits, and I'll show you a counterexample.

> 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. It's almost 
like you already know that as soon as you do I'll be able to post 
a counterexample, so you have to keep stalling.

-- 
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within