Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Moebius Newsgroups: sci.math Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary) Date: Fri, 6 Dec 2024 07:59:18 +0100 Organization: A noiseless patient Spider Lines: 24 Message-ID: References: <87frn50zjp.fsf@bsb.me.uk> <87y10vzo35.fsf@bsb.me.uk> <87ser3zgez.fsf@bsb.me.uk> Reply-To: invalid@example.invalid MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 06 Dec 2024 07:59:20 +0100 (CET) Injection-Info: dont-email.me; posting-host="264de29ac4942d9c683be6cd16be928f"; logging-data="2311344"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19Em8TOCo8Fo8XxPGq7UMyF" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:5GHIJO+bCZPvWqGAD/YL0Z8OlQk= In-Reply-To: Content-Language: de-DE Bytes: 2969 Am 06.12.2024 um 01:28 schrieb Chris M. Thomasson: > On 12/5/2024 5:40 AM, FromTheRafters wrote: >> WM used his keyboard to write : >>> On 05.12.2024 11:53, joes wrote: >>>> Am Thu, 05 Dec 2024 09:54:11 +0100 schrieb WM: >>>>> On 04.12.2024 20:59, Chris M. Thomasson wrote: >>>>> >>>>>> Not sure why WM thinks that Cantor Pairing does not work with any >>>>>> natural number... I think I am not misunderstanding WM here. >>>>> Take any natnumber you can. Almost all natnumbers are following. >>>>> Infinitely many of them cannot be "taken" or "given" and cannot be >>>>> proven to be in any mapping. But Cantor claims that all without any >>>>> exception can be taken. >>>> Yes, of course they can? Why shouldn't they? What does it mean to you? >>>> >>> All means all with no exception. But every number you can take >>> belongs to a vanishing subset of ℕ. >> >> What do you mean by vanishing? "vanishingly small" in comparison to the (infinite) rest. > Perhaps his brain in a toilet after a couple of flushes? Ugggh...