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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!news.mixmin.net!proxad.net!feeder1-2.proxad.net!usenet-fr.net!pasdenom.info!from-devjntp Message-ID: JNTP-Route: nemoweb.net JNTP-DataType: Article Subject: Re: How many different unit fractions are lessorequal than all unit =?UTF-8?Q?fractions=3F?= References: <73f09425214bb25768fabf576b4ae5d98ef97431@i2pn2.org> Newsgroups: sci.math JNTP-HashClient: 7YzWY7AklBRx7jMHkyHTiuAl8RQ JNTP-ThreadID: vb4rde$22fb4$2@solani.org JNTP-Uri: https://www.nemoweb.net/?DataID=Iz5zSuCuwslwe6r8CqsrwF8fszk@jntp User-Agent: Nemo/1.0 JNTP-OriginServer: nemoweb.net Date: Thu, 12 Sep 24 11:18:30 +0000 Organization: Nemoweb JNTP-Browser: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/128.0.0.0 Safari/537.36 Injection-Info: nemoweb.net; posting-host="2d3164039d34f770c4e7ff26535d32ded98f73cd"; logging-data="2024-09-12T11:18:30Z/9019388"; posting-account="217@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: 2134 Lines: 16 Le 12/09/2024 à 03:00, Richard Damon a écrit : > So, you can't "index" an unbounded set of unit fractions from 0, as > there isn't a "first" unit fraction from that end. > > We can "address" those unit fractions with the value, but we can not > "index" them from 0, only from 1/1. If you can index all unit fractions, then you can index them from every side. Fact is that NUF(x) increases from 0, but at no point it can inc4rease by more than 1 because of ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 Regards, WM