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Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: FromTheRafters <FTR@nomail.afraid.org> Newsgroups: sci.math Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary) Date: Thu, 05 Dec 2024 11:50:15 -0500 Organization: Peripheral Visions Lines: 16 Message-ID: <vislkd$1nn4k$1@dont-email.me> References: <vg7cp8$9jka$1@dont-email.me> <vier32$1madr$1@dont-email.me> <vierv5$1l1ot$2@dont-email.me> <viiqfd$2qq41$5@dont-email.me> <vijhrd$34mp8$1@dont-email.me> <vilh59$3k21l$5@dont-email.me> <vilheq$3ks01$3@dont-email.me> <vilhjk$3k21l$9@dont-email.me> <vilhk8$3ks01$4@dont-email.me> <vilhnl$3k21l$10@dont-email.me> <viljdo$3k21l$12@dont-email.me> <87frn50zjp.fsf@bsb.me.uk> <vinuvc$cdlu$1@dont-email.me> <vinvvu$c7p5$6@dont-email.me> <vio0u4$c7p5$8@dont-email.me> <vio8rj$ei97$5@dont-email.me> <vio9nu$f13q$1@dont-email.me> <vip1f1$npsr$2@dont-email.me> <vipaue$qd3r$1@dont-email.me> <87y10vzo35.fsf@bsb.me.uk> <vipf6v$qr8p$2@dont-email.me> <87ser3zgez.fsf@bsb.me.uk> <viqca6$12cut$2@dont-email.me> <virpnj$1g4uq$1@dont-email.me> <ff5ee533dd180eb24978c76e7e00ba6f4676d51a@i2pn2.org> <vis3iq$1iu5p$1@dont-email.me> <visafv$1kq6a$1@dont-email.me> <visi6v$1mmrh$1@dont-email.me> Reply-To: erratic.howard@gmail.com MIME-Version: 1.0 Content-Type: text/plain; charset="utf-8"; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 05 Dec 2024 17:50:21 +0100 (CET) Injection-Info: dont-email.me; posting-host="fd485c10c792450e6329c5a42bd0887d"; logging-data="1825940"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+zc/eHvu5prx7mPgEPiVeVRdfK83m2cbw=" Cancel-Lock: sha1:9dRnKvtf5TjpTabaGH2d+txUvoI= X-ICQ: 1701145376 X-Newsreader: MesNews/1.08.06.00-gb Bytes: 2348 WM pretended : > On 05.12.2024 14:40, FromTheRafters wrote: >> WM used his keyboard to write : > >>> 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? > > The subset of numbers that can be taken is ℕ_def. It is smaller than > |ℕ|/k for every k ∈ ℕ. > > Have you meanwhile found an example for sequences with terms a_n = b_n for > every n but different limit? Why should I?