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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!3.eu.feeder.erje.net!feeder.erje.net!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: <45ad1007-b1a7-49d0-a650-048f02738226@att.net> <9ef8dd8a-69be-44e2-bcf6-ea9c1fb30e21@att.net> <92189533-0c1f-4532-816f-564651cc8bf7@att.net> <155cdc8a628d47be1632791227bccf99425b1d5e@i2pn2.org> Newsgroups: sci.logic,sci.math JNTP-HashClient: d7_r7n5ptyp-eMCDiioOenDmAOM JNTP-ThreadID: KFm3f7lT2HjaTSiMfnv5xqZoSBw JNTP-Uri: http://news2.nemoweb.net/?DataID=en_fjxuLKegQPxOwdC8lXsKVbbI@jntp User-Agent: Nemo/0.999a JNTP-OriginServer: news2.nemoweb.net Date: Mon, 19 Aug 24 11:32:44 +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="2024-08-19T11:32:44Z/8992384"; 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: 2437 Lines: 24 Le 17/08/2024 à 16:29, Richard Damon a écrit : > On 8/17/24 9:28 AM, WM wrote: >> Le 16/08/2024 à 19:39, Jim Burns a écrit : >> >>> no element of ℕᵈᵉᶠ is its upper.end, >>> because >>> for each diminishable k >>> diminishable k+1 disproves by counter.example >>> that k is the upper.end of ℕᵈᵉᶠ >> >> SBZ(x) starts with 0 at 0 and increases, but at no point x it increases >> by more than 1 because of >> ∀n ∈ ℕ: 1/n - 1/(n+1) > 0. Therefore there is a smallest unit fractions >> and vice versa a greatest natnumber. >> What can't you understand? > But there is no point (>0) where it has a finite value, You can't see it and you are unable to derive it from mathematics. But blindness is not an argument. Regards, WM