Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: "Chris M. Thomasson" Newsgroups: sci.math Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary) Date: Sat, 7 Dec 2024 17:29:08 -0800 Organization: A noiseless patient Spider Lines: 25 Message-ID: References: <9bcc128b-dea8-4397-9963-45c93d1c14c7@att.net> <50c82b03-8aa1-492c-9af3-4cf2673d6516@att.net> <5a122d22-2b21-4d65-9f5b-4f226eebf9d4@att.net> <3af23566-0dfc-4001-b19b-96e5d4110fee@tha.de> <8a53c5d4-4afd-4f25-b1da-30d57e7fe91c@att.net> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 08 Dec 2024 02:29:08 +0100 (CET) Injection-Info: dont-email.me; posting-host="021479c43f8aee38ea8f1e7f736414c6"; logging-data="3597760"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19/loYqnZd4SEcL9Fg4Pmf4M69srnxzRkM=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:AEkBQO/7O1xT9ocaq+3eDvtKedE= In-Reply-To: Content-Language: en-US Bytes: 2707 On 12/7/2024 1:37 PM, WM wrote: > On 07.12.2024 20:59, Jim Burns wrote: >> On 12/7/2024 6:09 AM, WM wrote: >>> On 06.12.2024 19:17, Jim Burns wrote: >>>> On 12/6/2024 3:19 AM, WM wrote: >>>>> On 05.12.2024 23:20, Jim Burns wrote: >> >>>>>> ⎜ With {} NOT as an end.segment, >>>>> >>>>> all endsegments hold content. >>>> >>>> But no common.to.all finite.cardinals. >>> >>> Show two endsegments which >>> do not hold common content. >> >> I will, after you >> show me a more.than.finitely.many two. > > There are no more than finitely many natural numbers which can be shown. > All which can be shown have common content. [...] Huh? There are infinitely many natural numbers.