Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: Richard Heathfield <rjh@cpax.org.uk>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Sun, 6 Apr 2025 21:42:32 +0100
Organization: Fix this later
Lines: 26
Message-ID: <vsuovo$1o0kb$4@dont-email.me>
References: <vsn1fu$1p67k$1@dont-email.me>
 <7EKdnTIUz9UkpXL6nZ2dnZfqn_ednZ2d@brightview.co.uk>
 <vsng73$27sdj$1@dont-email.me>
 <gGKdnZiYPJVC03L6nZ2dnZfqn_udnZ2d@brightview.co.uk>
 <vsnk2v$2fc5a$1@dont-email.me> <vsnmtg$2i4qp$3@dont-email.me>
 <vsno7m$2g4cd$3@dont-email.me> <vsnp0o$2ka6o$2@dont-email.me>
 <vsnpv4$2g4cd$6@dont-email.me> <vsntes$2osdn$1@dont-email.me>
 <vsntv3$2paf9$1@dont-email.me> <vso1a0$2sf7o$1@dont-email.me>
 <vso2ff$2tj1d$2@dont-email.me> <vso3rj$2vems$2@dont-email.me>
 <vso4gh$2vg3b$1@dont-email.me> <vsqmlb$1ktm5$6@dont-email.me>
 <vsr1ae$1pr17$2@dont-email.me> <vst4nm$8daf$2@dont-email.me>
 <vsu9o4$lqc0$2@dont-email.me> <vsunj7$1redp$3@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Sun, 06 Apr 2025 22:42:33 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="dbe7ec1ac8ffd7a60b5ada94cfd55d95";
	logging-data="1835659"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+HFCnCKEZTU4RdkGdHZMETUbAQmkGEkqdkIMjmF7wl2g=="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:11BYUkjYxw36bpOqRHUXfVXGsF4=
Content-Language: en-GB
In-Reply-To: <vsunj7$1redp$3@dont-email.me>

On 06/04/2025 21:18, Lawrence D'Oliveiro wrote:
> On Sun, 6 Apr 2025 17:22:28 +0100, Andy Walker wrote:
> 
>> The constructed number will not continue to match any particular member
>> of the list indefinitely.
> 
> Congratulations, you got the point of my proof.
> 
> Isn’t the Cantor construction supposed to come up with a number not in the
> list, for *any* list?

It does.

For any list of N numbers, you can construct a number that 
differs in the nth digit from the nth number. That this works for 
finite lists is self-evident (suck it and see). It takes a little 
more thought to see that it also works for infinite lists, but it 
does. It just takes infinitely many steps, which is what makes 
the result incomputable..

-- 
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