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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: Sun, 29 Dec 2024 12:09:06 +0100 Organization: A noiseless patient Spider Lines: 14 Message-ID: <vkraki$tpqs$3@dont-email.me> References: <vg7cp8$9jka$1@dont-email.me> <vj9s4i$11a3p$1@dont-email.me> <vjam6d$1700v$1@dont-email.me> <vjc65g$1i9vk$3@dont-email.me> <vjf7kl$2s7e5$1@dont-email.me> <vjfmq3$2upa9$3@dont-email.me> <c6b624cb0b1b55d54aab969ee5b4e283ec7be3cd@i2pn2.org> <vjhp8b$3gjbv$1@dont-email.me> <dc9e7638be92c4d158f238f8c042c8559cd46521@i2pn2.org> <vjjg6p$3tvsg$1@dont-email.me> <c31edc62508876748c8cf69f93ab80c0a7fd84ac@i2pn2.org> <vjka3b$1tms$3@dont-email.me> <e11a34c507a23732d83e3d0fcde7b609cdaf3ade@i2pn2.org> <vjmse3$k2go$2@dont-email.me> <069069bf23698c157ddfd9b62b9b2f632b484c40@i2pn2.org> <vjooeq$11n0g$2@dont-email.me> <2d3620a6e2a8a57d9db7a33c9d476fe03cac455b@i2pn2.org> <vjrfcc$1m1b2$1@dont-email.me> <75921cc1f17cdb691969a99e666f237cd09c0b09@i2pn2.org> <vjsrp1$1tqvv$2@dont-email.me> <25729298b142c60d5b245231984119d42d4ac089@i2pn2.org> <vko14j$53b6$3@dont-email.me> <vko1vp$5mmo$1@dont-email.me> <vko2a3$5mmo$3@dont-email.me> <vkpkbr$fnhj$2@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Sun, 29 Dec 2024 12:09:06 +0100 (CET) Injection-Info: dont-email.me; posting-host="0a8d1c301754f45f71cb6cb758160409"; logging-data="976732"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18IZ6KSp5bdWg0gZtONKZQT4SCrBhEwM5A=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:rRpipLgI9kwZ2Z6OPQRP+a1qAFg= In-Reply-To: <vkpkbr$fnhj$2@dont-email.me> Content-Language: en-US Bytes: 2369 On 28.12.2024 20:42, Moebius wrote: >> Hint: For each and every n e IN there is a singleton such that n is in >> it (namely {n}). >> >> BUT there's no singleton such that each and every n e IN is in it. My theorem: Every union of FISONs which stay below a certain threshold stays below that threshold. Find a counterexample. Don't claim it but prove it. Fail. Regards, WM