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: Mon, 23 Dec 2024 12:18:22 +0100 Organization: A noiseless patient Spider Lines: 14 Message-ID: References: <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> <0393b227-fa2e-4649-a363-e53ab6e73327@att.net> <1e19b1be-00eb-4f2a-ba97-e66aa395b56b@att.net> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 23 Dec 2024 12:18:23 +0100 (CET) Injection-Info: dont-email.me; posting-host="f76a164e5de1a13044de2f0c205d5b55"; logging-data="1242640"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+FxnQvKWorOTB1Zz8ifziSzJehJ8uuAq0=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:fZWAPUroCwdyr2uLQvEQhytv+wM= In-Reply-To: <1e19b1be-00eb-4f2a-ba97-e66aa395b56b@att.net> Content-Language: en-US Bytes: 2392 On 23.12.2024 12:02, Jim Burns wrote: > > The empty limit set is caused by > each finiteⁿᵒᵗᐧᵂᴹ.cardinal being not.in > almost all of the end.segments > (in only finitely.many end.segment.exceptions) And why is this so? Because every endsegment removes exactly one number from the content. There is a bijection between endsegments and removed numbers. Regards, WM