Path: ...!news.tomockey.net!news.samoylyk.net!news.quux.org!eternal-september.org!feeder3.eternal-september.org!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 08:03:44 -0000 (UTC)
Organization: A noiseless patient Spider
Lines: 12
Message-ID: <vso3ov$2vems$1@dont-email.me>
References: <vsn1fu$1p67k$1@dont-email.me> <vso3j4$2vbn4$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit
Injection-Date: Fri, 04 Apr 2025 10:03:44 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="a838268cadc40d8a0ecf633714aea4dd";
	logging-data="3128028"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+mdbMShnWNLQFxooPuTmqd"
User-Agent: Pan/0.162 (Pokrosvk)
Cancel-Lock: sha1:UiHZ+t7ed+lTktxQkXFUpInPTvI=
Bytes: 1453

On Fri, 4 Apr 2025 11:00:36 +0300, Mikko wrote:

> On 2025-04-03 22:18:38 +0000, Lawrence D'Oliveiro said:
> 
>> The Cantor diagonal construction is an algorithm for computing an
>> incomputable number.
> 
> Can you prove that it computes an incomputable number?

It’s trying to come up with a number that cannot fit into a set with 
cardinality ℵ₀. The cardinality of the computable numbers is the same as 
that of the integers, which is ℵ₀.