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Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!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, effectively) Date: Thu, 2 Jan 2025 12:50:37 +0100 Organization: A noiseless patient Spider Lines: 18 Message-ID: <vl5uid$3au1p$1@dont-email.me> References: <vg7cp8$9jka$1@dont-email.me> <bce1b27d-170c-4385-8938-36805c983c49@att.net> <vk693m$f52$2@dont-email.me> <a17eb8b6-7d11-4c59-b98c-b4d5de8358ca@att.net> <vk7dmb$7mh2$2@dont-email.me> <b72490c1-e61a-4c23-a3a5-f624b2c084e4@att.net> <vk8tbq$j9h1$1@dont-email.me> <bd7dfdc7-6471-4fe6-b078-0ca739031580@att.net> <vklumc$3htmt$1@dont-email.me> <c03cf79d-0572-4b19-ad92-a0d12df53db9@att.net> <n9CdnR02SsevtPL6nZ2dnZfqnPidnZ2d@giganews.com> <45a632ed-26cc-4730-a8dd-1e504d6df549@att.net> <vkpa98$dofu$2@dont-email.me> <3d2fe306aa299bc78e94c14dadd21645d8db9829@i2pn2.org> <vkr8sq$t59a$2@dont-email.me> <d4669f26483b01c8a43dfd3ac4b61ab4a42bf551@i2pn2.org> <vksikk$17fjt$1@dont-email.me> <aa2941e93e806f1dda55d563dd062db67eb879f1@i2pn2.org> <vktmi3$1ia1u$1@dont-email.me> <c46775b30460bc564b3fe7bd1b838713829024f8@i2pn2.org> <vkv3t1$1qb93$1@dont-email.me> <2163aa0c0efba66c813e8ebda5ef5ece6d19ea34@i2pn2.org> <vl1bp4$2bcos$2@dont-email.me> <4d797c9134ea480aa4976cf866cacaede8d309bd@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 02 Jan 2025 12:50:37 +0100 (CET) Injection-Info: dont-email.me; posting-host="a3e4916d82901f495981bca5b3dfcc34"; logging-data="3504185"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+3RSUtz8RfVkR8wLd6ftZXlWYiY6iD70Y=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:U6tnIsanX4fIJJ0N3wxYPlxaWjY= Content-Language: en-US In-Reply-To: <4d797c9134ea480aa4976cf866cacaede8d309bd@i2pn2.org> Bytes: 2684 On 01.01.2025 14:51, joes wrote: > Am Tue, 31 Dec 2024 19:05:24 +0100 schrieb WM: >> I don't stop but know that every FISON is finite as its name says and >> covers at most 1 % of ℕ. > Yes, you stop at some finite threshold. Go farther. Find a FISON that is not below 1 %. > >> You cannot find a natural number that isn't in a FISON. But there must >> be more because FISONs cover less than 1 % of ℕ. > No??? There are infinitely many of them, and together they form N. Stupid belief. Every union of FISONs which stay below a certain threshold stays below that threshold. Regards, WM