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Path: ...!2.eu.feeder.erje.net!feeder.erje.net!proxad.net!feeder1-2.proxad.net!usenet-fr.net!pasdenom.info!from-devjntp Message-ID: <dVNyc7MMp5G7UOSEcqTzh_UWDPI@jntp> JNTP-Route: news2.nemoweb.net JNTP-DataType: Article Subject: Re: how References: <qHqKnNhkFFpow5Tl3Eiz12-8JEI@jntp> <vJvCxLOj98F4nrRmEh2M6dyGkSc@jntp> <v3st0i$1jtfh$1@dont-email.me> <hZvnfi5EsOcLQp4jywf9ecNmAW8@jntp> <v4cvqt$1qbpc$3@dont-email.me> <marAIk0bzCCe6m7qluPLtxzZ0Zw@jntp> <v4d1pc$1qq74$2@dont-email.me> <9HunCi0heOernIpLiINDMDau01o@jntp> <v4d2f7$1qq74$5@dont-email.me> <v4d2hd$1qq74$6@dont-email.me> Newsgroups: sci.math JNTP-HashClient: T6yyVoBqPbjsJEuQ6Skx-vNBaZA JNTP-ThreadID: 4YLc1knY-8u5i_KQ0oWqy89D7aY JNTP-Uri: http://news2.nemoweb.net/?DataID=dVNyc7MMp5G7UOSEcqTzh_UWDPI@jntp User-Agent: Nemo/0.999a JNTP-OriginServer: news2.nemoweb.net Date: Thu, 13 Jun 24 10:48:38 +0000 Organization: Nemoweb JNTP-Browser: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/125.0.0.0 Safari/537.36 Injection-Info: news2.nemoweb.net; posting-host="25d5a506365fc8262443ce1bd287e5d0233c1bef"; logging-data="2024-06-13T10:48:38Z/8899979"; 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: 2557 Lines: 27 Le 12/06/2024 à 23:04, "Chris M. Thomasson" a écrit : > On 6/12/2024 2:03 PM, Chris M. Thomasson wrote: >> On 6/12/2024 1:58 PM, WM wrote: >>> Le 12/06/2024 à 22:51, "Chris M. Thomasson" a écrit : >>>> On 6/12/2024 1:38 PM, WM wrote: >>>>> >>>>> Yes, it is impossible to find a last one before ω. >>>> >>>> Indeed. You are correct here. There is no last dark number? >>> >>> There is one (think of the first unit fraction) but as it is and >>> remains dark, it cannot be caught. >> >> I thought there were infinitely many dark natural numbers? If so, how >> can there possibly be a largest dark number? >> > > You told me that there are indeed infinitely many dark natural numbers, > right? > Yes. You cannot get to the end because dark numbers have no discernible order. Fact is: If we assume the existence of ω at the ordinal line, then something must exist before, either dark numbers or nothing. There is no third alternative. Or can you imagine one? Regards, WM