Path: ...!feeds.phibee-telecom.net!weretis.net!feeder8.news.weretis.net!pasdenom.info!from-devjntp Message-ID: <5cjx16x9QcPy_u3MHizdiDCz_W8@jntp> JNTP-Route: news2.nemoweb.net JNTP-DataType: Article Subject: Re: how References: <9584f51f-5d90-4270-b763-b5102b2d6e2f@att.net> <6350e436-cfa4-427d-989e-1b0d42814aae@att.net> <673764b9-69b9-41a2-ab82-bf90d8dee8e8@att.net> Newsgroups: sci.math JNTP-HashClient: F3hXSHI8gVrgKb6m8d2alpFeZO4 JNTP-ThreadID: 4YLc1knY-8u5i_KQ0oWqy89D7aY JNTP-Uri: http://news2.nemoweb.net/?DataID=5cjx16x9QcPy_u3MHizdiDCz_W8@jntp User-Agent: Nemo/0.999a JNTP-OriginServer: news2.nemoweb.net Date: Tue, 04 Jun 24 14:10:43 +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="2024-06-04T14:10:43Z/8887624"; 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: 2723 Lines: 41 Le 04/06/2024 à 04:07, Jim Burns a écrit : > On 6/3/2024 3:50 PM, WM wrote: > Assumption (2.) describes > objects in our familiar arithmetic. That is true because our familiar arithmetic is based upon potential infinity. Only in finished infinity dark numbers are required. > For each n in ℕ⁺ > n countable.to from.0 > n+1 is countable.to from.n > n+1 is countable.to from.0 through.n > n+1 is in ℕ⁺ > n is not larger than all numbers in ℕ⁺ And in particular all n have ℵo dark successors. > 𝔼 is the subset of even numbers in ℕ⁺ > 𝕆 is the subset of odd numbers in ℕ⁺ > > ⎛ There is no number in 𝔼 larger than > ⎝ all numbers in 𝕆 > > ⎛ There is no number in 𝕆 larger than > ⎝ all numbers in 𝔼 Dark numbers do not unveil their mystery. But from NUF we can prove that a first one must exist although we cannot find it. >> Only one of the two complementary sets >> can and must contain the first point. > > Why? > Responding "Logic" or "Mathematics" is dodging. But it is true. Like Bob's survival. Regards, WM