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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!feeder3.eternal-september.org!news.eternal-september.org!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, effectively) Date: Sun, 29 Dec 2024 23:31:46 +0100 Organization: A noiseless patient Spider Lines: 17 Message-ID: References: <7356267c-491b-45c2-b86a-d40c45dfa40c@att.net> <4bf8a77e-4b2a-471f-9075-0b063098153f@att.net> <31180d7e-1c2b-4e2b-b8d6-e3e62f05da43@att.net> <45a632ed-26cc-4730-a8dd-1e504d6df549@att.net> <3d2fe306aa299bc78e94c14dadd21645d8db9829@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 29 Dec 2024 23:31:48 +0100 (CET) Injection-Info: dont-email.me; posting-host="ff0632a573d885e48e5fae2ba6c0d15b"; logging-data="1293949"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18cFR6R5M8xriPlVazgkabzNEnrIhaT3ac=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:hf54hzdluDhpcDuOBbrzVfhyqx8= In-Reply-To: Content-Language: en-US Bytes: 2615 On 29.12.2024 22:27, joes wrote: > Am Sun, 29 Dec 2024 11:39:22 +0100 schrieb WM: >> A relative size is very useful in order to correct the fantasy claim >> that the union of all FISONs covers the infinite gap between all FISONs >> and ω. > There is no gap. If all FISONs are finite and followed by infinite endsegments, then there is an infinite gap. 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