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Path: ...!news.nobody.at!weretis.net!feeder8.news.weretis.net!pasdenom.info!from-devjntp Message-ID: <KGy4lqRYh8Vx92Fmggj5UgU6SeM@jntp> JNTP-Route: news2.nemoweb.net JNTP-DataType: Article Subject: Re: There is a first/smallest integer (in =?UTF-8?Q?M=C3=BCckenland=29?= References: <v78aei$1qhrg$2@dont-email.me> <iez0JhnP5QUwPTJ47oubeE1Aq5M@jntp> <d1dcd124f2f0194900fc641c7c54043ed9744144@i2pn2.org> Newsgroups: sci.math JNTP-HashClient: dQMfTFj7EwUMtPk-KPnvMCuByeA JNTP-ThreadID: v78aei$1qhrg$2@dont-email.me JNTP-Uri: http://news2.nemoweb.net/?DataID=KGy4lqRYh8Vx92Fmggj5UgU6SeM@jntp User-Agent: Nemo/0.999a JNTP-OriginServer: news2.nemoweb.net Date: Thu, 18 Jul 24 13:28:13 +0000 Organization: Nemoweb JNTP-Browser: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/126.0.0.0 Safari/537.36 Injection-Info: news2.nemoweb.net; posting-host="82b75c1d0a83e677ff646b52485f72f8b23749df"; logging-data="2024-07-18T13:28:13Z/8953707"; 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: 2070 Lines: 23 Le 18/07/2024 à 04:15, Richard Damon a écrit : > On 7/17/24 10:43 AM, WM wrote: >> Can you explain how NUF(x) can increase from 0 to many more in one point >> x although all unit fractions are separated by finite distances of >> uncountably many x each? >> > Because is isn't a properly defined function. What do you miss in its definition? > > It has no finite value for any finite value of x > 0. Then basic mathematics is false. ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 shows that every unit fraction occupies its own point. > > Thus, one need no figure how it gets from 0 to any other number, since > it doesn't. Does it go from 0 to ℵo? How can that happen? Regards, WM