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Path: ...!weretis.net!feeder8.news.weretis.net!pasdenom.info!from-devjntp Message-ID: <D3wXtU4oUb8LWXofzT1WiChqmfE@jntp> JNTP-Route: news2.nemoweb.net JNTP-DataType: Article Subject: Re: how References: <qHqKnNhkFFpow5Tl3Eiz12-8JEI@jntp> <uv7609$n6lm$2@i2pn2.org> <0i01kKYhCcWwtJURV35AV3Oy16s@jntp> <44eaef1b-35be-4b50-900b-52b010ba9aa0@att.net> <_g9BcdiKQ1epFrcvM4FSF2rZkN8@jntp> <f4890eb5-e8df-4d98-a1ba-98c40f516df5@att.net> <HowGC2OIbH3GwJcRQBgR51F0vzM@jntp> <29c99292-805f-4f34-a1c8-ce1c7cd82f75@att.net> <WUdrtFzAGxMxA0R9q5J6yKSUZZk@jntp> <7966ba6c-62aa-4479-8ce1-cba203d36049@att.net> Newsgroups: sci.math JNTP-HashClient: LpeBOy8ca4V6MbtyliqRwndhigA JNTP-ThreadID: 4YLc1knY-8u5i_KQ0oWqy89D7aY JNTP-Uri: http://news2.nemoweb.net/?DataID=D3wXtU4oUb8LWXofzT1WiChqmfE@jntp User-Agent: Nemo/0.999a JNTP-OriginServer: news2.nemoweb.net Date: Mon, 15 Apr 24 11:59:04 +0000 Organization: Nemoweb JNTP-Browser: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/123.0.0.0 Safari/537.36 Injection-Info: news2.nemoweb.net; posting-host="649daec9527d00fb227e738c133438fae4eb4c2e"; logging-data="2024-04-15T11:59:04Z/8817863"; 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: 2756 Lines: 44 Le 14/04/2024 à 22:39, Jim Burns a écrit : > On 4/14/2024 3:12 PM, WM wrote: >> Le 13/04/2024 à 21:16, Jim Burns a écrit : > >>> if n < ω >>> then 2⋅n < ω >> >> That is impossible because >> doubling is a linear operation. > > You (WM) have decided that > ω is like all the numbers n < ω Cantor has decided, that ω is an ordinal which can be counted and passed by counting (Hilbert). > > Whatever it might mean > to put ω and 1 on the same line, It is Cantor's number classes. See Transfinity p. 42. > > If n is a number > different.in.size from its nearest.neighbors, > then 2⋅n is a number > different.in.size from its nearest.neighbors. > > If n is a number less than > the least.upper.bound of numbers > different.in.size from their nearest.neighbors, > then 2⋅n is a number less than > the least.upper.bound of numbers > different.in.size from their nearest.neighbors. That is wrong if all natnumbers are present already such that no further natnumbers fits below ω. > > If n < ω > then 2⋅n < ω That is true if not all natnumbers are present, blocking all places for finite ordinals. Regards, WM