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Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: WM <wolfgang.mueckenheim@tha.de> 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: <vkbgtu$15tgg$1@dont-email.me> References: <vg7cp8$9jka$1@dont-email.me> <vjmgdm$i9be$1@dont-email.me> <abf7344d-b95b-4432-8626-8356dc1dd261@att.net> <vjn9ud$mlgt$2@dont-email.me> <4051acc5-d00a-40d2-8ef7-cf2b91ae75b6@att.net> <vjreik$1lokm$1@dont-email.me> <8d69d6cd-76bc-4dc1-894e-709d044e68a1@att.net> <vjst0u$1tqvv$3@dont-email.me> <7356267c-491b-45c2-b86a-d40c45dfa40c@att.net> <vjufr6$29khr$3@dont-email.me> <4bf8a77e-4b2a-471f-9075-0b063098153f@att.net> <vjv6uv$2dra0$1@dont-email.me> <31180d7e-1c2b-4e2b-b8d6-e3e62f05da43@att.net> <vk1brk$2srss$7@dont-email.me> <bb80c6c5-04c0-4e2d-bb21-ac51aab9e252@att.net> <vk23m7$31l8v$1@dont-email.me> <bce1b27d-170c-4385-8938-36805c983c49@att.net> <vk693m$f52$2@dont-email.me> <a17eb8b6-7d11-4c59-b98c-b4d5de8358ca@att.net> <vk7dmb$7mh2$2@dont-email.me> <b72490c1-e61a-4c23-a3a5-f624b2c084e4@att.net> <vk8tbq$j9h1$1@dont-email.me> <0393b227-fa2e-4649-a363-e53ab6e73327@att.net> <vka3i4$q8gm$1@dont-email.me> <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