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Path: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: WM <wolfgang.mueckenheim@tha.de> Newsgroups: sci.logic Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary) Date: Thu, 28 Nov 2024 15:17:49 +0100 Organization: A noiseless patient Spider Lines: 23 Message-ID: <vi9u2d$ig6a$1@dont-email.me> References: <31419fde-62b3-46f3-89f6-a48f1fe82bc0@att.net> <vhn1jk$jf6v$1@dont-email.me> <vhn3po$jvo1$1@dont-email.me> <vhn420$jf6v$3@dont-email.me> <vhpg51$13soc$1@dont-email.me> <vhpnrb$15239$1@dont-email.me> <vhs2gn$1kjtc$1@dont-email.me> <vhs4ue$1ku9t$1@dont-email.me> <vhv6or$280s6$1@dont-email.me> <vhvbjb$28n6o$1@dont-email.me> <vi1dbj$2moon$1@dont-email.me> <vi224l$2pgrd$1@dont-email.me> <vi4383$3csd4$2@dont-email.me> <vi4a6c$3dt4s$2@dont-email.me> <c5a03e73203e6409f6b50c25b84a22d8df0d210b@i2pn2.org> <vi4k5a$3fj1t$1@dont-email.me> <8b860c66587b6d5d18e565caddb42cc3d5bb813c@i2pn2.org> <vi4vg4$3hg8t$3@dont-email.me> <vi509b$3hqcp$1@dont-email.me> <vi56el$3is82$1@dont-email.me> <vi57p2$3j62u$1@dont-email.me> <vi6tu2$3v0dn$3@dont-email.me> <bedba0f79694c3adbbcb4eff22a28b9597ea1293@i2pn2.org> <vi7uam$5cmb$1@dont-email.me> <376546bee4809e20528e0e9481315611ec5c3848@i2pn2.org> <vi9n75$hepc$1@dont-email.me> <659cb7a16573c854e96c7a982fe8b15397fb1210@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Thu, 28 Nov 2024 15:17:49 +0100 (CET) Injection-Info: dont-email.me; posting-host="67cce382144bf1df261eb72066b481f0"; logging-data="606410"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/D5q+hgw8NOtZjIDdqKeN0OOtJyAVUfX0=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:oBrvfHqZkmdbyq7yP4D/gNGbqkc= Content-Language: en-US In-Reply-To: <659cb7a16573c854e96c7a982fe8b15397fb1210@i2pn2.org> Bytes: 2842 On 28.11.2024 14:01, Richard Damon wrote: > On 11/28/24 7:20 AM, WM wrote: >> On 27.11.2024 22:20, Richard Damon wrote: >>> On 11/27/24 3:09 PM, WM wrote: >> >>>> It is completed! Every number 10n starts wit a black hat. >>> >>> Right, and it gives that hat to n, so every number gets one. >>> >>> And, 10n will get back a hat from 100n, so it still have one at the end. >>> >> It seems so, but that is impossible. Up to every 10n, the interval 1, >> 2, 3, ... 10n has a covering of 1/10 only. The limit of this sequence >> is 1/10 too. And since this is true for all natural numbers, where >> should additional hats come from? > No, it is possilbe, It is impossible that the sequence 1/10, 1/10, 1/10, ... has another limit than 1/10. Regards, WM