Path: ...!weretis.net!feeder8.news.weretis.net!pasdenom.info!from-devjntp Message-ID: JNTP-Route: news2.nemoweb.net JNTP-DataType: Article Subject: Re: Replacement of Cardinality References: <9xKV2FrNFAjW0MsxhKvnP9dPB4w@jntp> <8G0IFYrPqHdBEH1pzbz9ifVRvd0@jntp> <11698e94cb8361b62f1686b64d6351a9720d4d3d@i2pn2.org> <1b259a91952c93a56ad1e0063a2d7440aed185f2@i2pn2.org> <36aabaae939b651d51ae9dfba57c1f4a3c032447@i2pn2.org> Newsgroups: sci.logic,sci.math JNTP-HashClient: 70U_Ijs6Fs979oYwXcduQAraAfk JNTP-ThreadID: KFm3f7lT2HjaTSiMfnv5xqZoSBw JNTP-Uri: http://news2.nemoweb.net/?DataID=SYjKjdOLonJDxelTnBkxOxmRO7Y@jntp User-Agent: Nemo/0.999a JNTP-OriginServer: news2.nemoweb.net Date: Thu, 01 Aug 24 12:02:52 +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="2024-08-01T12:02:52Z/8971669"; 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 Bytes: 3152 Lines: 37 Le 31/07/2024 à 18:20, joes a écrit : > Am Wed, 31 Jul 2024 14:27:06 +0000 schrieb WM: >> Le 31/07/2024 à 03:28, Richard Damon a écrit : >>> On 7/30/24 1:37 PM, WM wrote: >>>> Le 30/07/2024 à 03:18, Richard Damon a écrit : >>>>> On 7/29/24 9:11 AM, WM wrote: >>>> >>>>>>> But what number became ω when doubled? >>>> ω/2 >>> And where is that in {1, 2, 3, ... w} ? >> In the midst, far beyond all definable numbers, far beyond ω/10^10. > That is a bit imprecise. Even though you keep on talking about > consecutive infinities, you can't compare natural and "dark" numbers. Dark natnumbers are larger than defined natnumbers. Even dar natnumbers can be compared by size. ω/10^10 < ω/10 < ω/2, < ω-1. >> ω/10^10 and ω/10 are dark natural numbers. >> >>>>>> If all natural numbers exist, then ω-1 exists. >>>>> Why? >>>> Because otherwise there was a gap below ω. >>> But you combined two different sets, so why can't there be a gap? >> I assume completness. > Completeness of N? No number n reaches omega. What is immediately before ω? Is it a blasphemy to ask such questions? > >>>> ∀n ∈ ℕ: 1/n - 1/(n+1) > 0. Note the universal quantifier. >>> Right, so we can say that ∀n ∈ ℕ: 1/n > 1/(n+1), so that for every unit >>> fraction 1/n, there exists another unit fraction smaller than itself. >> No. My formula says ∀n ∈ ℕ. > That is not a contradiction. It is not a contradiction to my formula if some n has no n+1. Regards, WM