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From: Richard Heathfield <rjh@cpax.org.uk>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Fri, 4 Apr 2025 06:16:20 +0100
Organization: Fix this later
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On 04/04/2025 06:00, Lawrence D'Oliveiro wrote:
> On Fri, 4 Apr 2025 05:46:46 +0100, Richard Heathfield wrote:
> 
>> On 04/04/2025 05:24, Lawrence D'Oliveiro wrote:
>>
>>> At every point, the probability that the N digits computed so far match
>>> some number later in the list is 1.
>>
>> Counter-example follows.
>>
>> Input list:
>>
>> 1111
>> 2222
>> 3333
>> 4444
> 
> Is that all? Just 4 numbers?

The Cantor diagonal argument shows that *any* list, finite or 
infinite, is incomplete. If you would prefer to illustrate your 
point using an infinite list that's fine by me, but even at 
100Mbps it's going to take a while to upload to your news server.

If you do go for an infinite list, bear in mind that there are 
infinitely many infinite lists. For every set of N digits you can 
construct such that "at every point, the probability that the N 
digits computed so far match some number later in the list is 1", 
I can define an infinite list that doesn't contain it.

-- 
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