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Path: ...!npeer.as286.net!npeer-ng0.as286.net!weretis.net!feeder8.news.weretis.net!pasdenom.info!from-devjntp Message-ID: <w2KNEc6WpgYmvVtoH_VZTRkLnUg@jntp> JNTP-Route: news2.nemoweb.net JNTP-DataType: Article Subject: Re: Replacement of Cardinality References: <hsRF8g6ZiIZRPFaWbZaL2jR1IiU@jntp> <P04FAosjolyjDfgV0JPXWx1mF6o@jntp> <40165884-df8f-4614-8644-9161d72fd1cb@att.net> <-qUZ96ARwcjh9QPfyWRnijjNwoY@jntp> <6b837540-3d9a-4b8e-9a70-88d52e81a1a4@att.net> <xQQT0K_Q_k2FbMcCUXF8j3CEg84@jntp> <9822f5da-d61e-44ba-9d70-2850da971b42@att.net> <p36L63dXamDAkHDhkZhDKqx-h-o@jntp> <d8bbe664-a601-4590-9a7f-d5312b4dae54@att.net> <v8j55c$2u09m$2@dont-email.me> Newsgroups: sci.logic,sci.math JNTP-HashClient: lbVBmNwJtCxQz4f1laoj-WGkPQQ JNTP-ThreadID: KFm3f7lT2HjaTSiMfnv5xqZoSBw JNTP-Uri: http://news2.nemoweb.net/?DataID=w2KNEc6WpgYmvVtoH_VZTRkLnUg@jntp User-Agent: Nemo/0.999a JNTP-OriginServer: news2.nemoweb.net Date: Sat, 03 Aug 24 14:25:03 +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="2024-08-03T14:25:03Z/8974184"; 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: 2217 Lines: 15 Le 02/08/2024 à 19:31, Moebius a écrit : > For each and every of these points [here referred to with the > variable "x"]: NUF(x) = ℵ₀ . I recognized lately that you use the wrong definition of NUF. Here is the correct definition: There exist NUF(x) unit fractions u, such that for all y >= x: u < y. Note that the order is ∃ u ∀ y. NUF(x) = ℵ₀ for all x > 0 is wrong. NUF(x) = 1 for all x > 0 already is wrong since there is no unit fraction smaller than all unit fractions. ℵ₀ unit fractions need ℵ₀*2ℵ₀ points above zero. Regards, WM