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: Sun, 29 Dec 2024 12:09:06 +0100 Organization: A noiseless patient Spider Lines: 14 Message-ID: References: <069069bf23698c157ddfd9b62b9b2f632b484c40@i2pn2.org> <2d3620a6e2a8a57d9db7a33c9d476fe03cac455b@i2pn2.org> <75921cc1f17cdb691969a99e666f237cd09c0b09@i2pn2.org> <25729298b142c60d5b245231984119d42d4ac089@i2pn2.org> 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: 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