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Path: ...!eternal-september.org!feeder3.eternal-september.org!news.gegeweb.eu!gegeweb.org!pasdenom.info!from-devjntp Message-ID: <sglIw8p3PCeHivaAhg-7IVZCN4A@jntp> JNTP-Route: news2.nemoweb.net JNTP-DataType: Article Subject: Re: Replacement of Cardinality References: <hsRF8g6ZiIZRPFaWbZaL2jR1IiU@jntp> <f920592b-897c-48b9-a9af-80f25bc60e4b@att.net> <DDPks1ynTy6IhIWNHaxt25GM1v0@jntp> <6c471296-90b8-4cf7-bc9b-480bd34ef190@att.net> <v93n0s$b7a2$4@dont-email.me> <1f25a3d6-7b0e-476d-aa99-ecb003cf763f@att.net> <b0XFTJvTommasLo9Ns10OeW0TN0@jntp> <75e2ce0e-7df8-4266-968b-9c58e4140b03@att.net> <RCAlRuRy_RKB_tYItKJs7fNcIs0@jntp> <35d8c0a1-dab3-4c15-8f24-068e8200cb07@att.net> Newsgroups: sci.logic,sci.math JNTP-HashClient: Fzt00Z7aPgnnAZkGayMgCdZMlys JNTP-ThreadID: KFm3f7lT2HjaTSiMfnv5xqZoSBw JNTP-Uri: http://news2.nemoweb.net/?DataID=sglIw8p3PCeHivaAhg-7IVZCN4A@jntp User-Agent: Nemo/0.999a JNTP-OriginServer: news2.nemoweb.net Date: Mon, 12 Aug 24 13:50:09 +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="2024-08-12T13:50:09Z/8983983"; 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: 2161 Lines: 23 Le 11/08/2024 à 19:56, Jim Burns a écrit : > On 8/11/2024 8:29 AM, WM wrote: >>> What causes an exception: nₓ ∈ ℕ without ⅟(nₓ+1) ? >> >> The end of the positivee axis. > >>>> ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 > > ∀n ∈ ℕ: 1/n > 1/(n+1) > 0 If 1/(n+1) exists. > > Each positive unit fraction is not > the first positive unit fraction. > > What causes an exception: nₓ ∈ ℕ: > ⅟nₓ > 0 without ⅟(nₓ+1) > 0 ? The end of the positive axis. Regards, WM