Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: WM Newsgroups: sci.math Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary) Date: Sun, 22 Dec 2024 14:07:47 +0100 Organization: A noiseless patient Spider Lines: 13 Message-ID: References: <6c74c2e9-17d7-4eb4-afcd-c058309b6c8a@tha.de> <4327ba4a-e810-4565-83e8-b9572018ac35@att.net> <4051acc5-d00a-40d2-8ef7-cf2b91ae75b6@att.net> <8d69d6cd-76bc-4dc1-894e-709d044e68a1@att.net> <7356267c-491b-45c2-b86a-d40c45dfa40c@att.net> <4bf8a77e-4b2a-471f-9075-0b063098153f@att.net> <31180d7e-1c2b-4e2b-b8d6-e3e62f05da43@att.net> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Sun, 22 Dec 2024 14:07:48 +0100 (CET) Injection-Info: dont-email.me; posting-host="779124b0f9eb435d01e5c1ff507e7f96"; logging-data="673355"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1//G1C5nJ1nct8mHZZ6GUxRxC8FFSx8Rmo=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:8398kMLSdCJisK6x9Xd55ddMUnc= In-Reply-To: Content-Language: en-US Bytes: 2471 On 22.12.2024 13:28, Richard Damon wrote: > On 12/21/24 4:58 PM, WM wrote: >> Finite endsegments have a natural number of elements. > > SO, none of your E(n) are finite endsegments, since they all have an > INFINITE number of elements, being the INFINITE set of > { n+1, n+2, n+3, ... } by your definition. The intersection of all endsegments is empty. It cannot get empty other than by one element per endsegment. Regards, WM