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Path: ...!feeds.phibee-telecom.net!3.eu.feeder.erje.net!feeder.erje.net!usenet.goja.nl.eu.org!pasdenom.info!from-devjntp Message-ID: <-qUZ96ARwcjh9QPfyWRnijjNwoY@jntp> JNTP-Route: news2.nemoweb.net JNTP-DataType: Article Subject: Re: Replacement of Cardinality References: <hsRF8g6ZiIZRPFaWbZaL2jR1IiU@jntp> <881fc1a1-2e55-4f13-8beb-94d1f941b5af@att.net> <vg44QVKbPSR4U0Tq71L-fg5yqgM@jntp> <85194aeb-1b24-4486-8bcc-4dcd43b4fd2f@att.net> <VPcfM2gW_CIIfddmzwBYPrpt87w@jntp> <f3089a55-39f4-4df1-a525-58e21342ced8@att.net> <P04FAosjolyjDfgV0JPXWx1mF6o@jntp> <40165884-df8f-4614-8644-9161d72fd1cb@att.net> Newsgroups: sci.logic,sci.math JNTP-HashClient: qaUX7bEpVBCjcSot7moqeEfipvg JNTP-ThreadID: KFm3f7lT2HjaTSiMfnv5xqZoSBw JNTP-Uri: http://news2.nemoweb.net/?DataID=-qUZ96ARwcjh9QPfyWRnijjNwoY@jntp User-Agent: Nemo/0.999a JNTP-OriginServer: news2.nemoweb.net Date: Wed, 31 Jul 24 13:59:36 +0000 Organization: Nemoweb JNTP-Browser: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/127.0.0.0 Safari/537.36 Injection-Info: news2.nemoweb.net; posting-host="82b75c1d0a83e677ff646b52485f72f8b23749df"; logging-data="2024-07-31T13:59:36Z/8970542"; posting-account="217@news2.nemoweb.net"; mail-complaints-to="julien.arlandis@gmail.com" JNTP-ProtocolVersion: 0.21.1 JNTP-Server: PhpNemoServer/0.94.5 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-JNTP-JsonNewsGateway: 0.96 From: WM <wolfgang.mueckenheim@tha.de> Bytes: 1886 Lines: 10 Le 30/07/2024 à 20:37, Jim Burns a écrit : > NUF(x) = |⅟ℕ∩(0,x]| = ℵ₀ > does not imply any unit fraction outside (0,x] But it implies that you can use only x having ℵ₀ smaller positive points, in fact even ℵ₀*2ℵ₀. ∀ x > 0: NUF(x) = ℵ₀ would be wrong. Regards, WM