Warning: mysqli::__construct(): (HY000/1203): User howardkn already has more than 'max_user_connections' active connections in D:\Inetpub\vhosts\howardknight.net\al.howardknight.net\includes\artfuncs.php on line 21
Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!weretis.net!feeder8.news.weretis.net!pasdenom.info!from-devjntp Message-ID: 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: <7mXj2D8kEhAscu3HLTqTUKsaj18@jntp> Newsgroups: sci.math JNTP-HashClient: IwN5iwyprmSrB_c_k_JDEKr0_X4 JNTP-ThreadID: v78aei$1qhrg$2@dont-email.me JNTP-Uri: http://news2.nemoweb.net/?DataID=Eb-CQaKSaHkMpWykEcQGtifvbV0@jntp User-Agent: Nemo/0.999a JNTP-OriginServer: news2.nemoweb.net Date: Wed, 17 Jul 24 17:17:54 +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="2024-07-17T17:17:54Z/8952670"; 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: 2412 Lines: 29 Le 17/07/2024 à 19:01, joes a écrit : > Am Wed, 17 Jul 2024 15:08:30 +0000 schrieb WM: >> Le 17/07/2024 à 16:56, Moebius a écrit : >>> Am 17.07.2024 um 16:43 schrieb WM: >> >>>> Can you explain how NUF(x) can [jump] from 0 [at x = 0] to [aleph_0] >>>> [at any] >>>> point x [> 0] although all unit fractions are separated by finite >>>> distances [...] >>> >>> Yes, of course: For each and every x e IR, x > 0 there are >>> countably-infinitely many unit fractions which are <= x. (Hint: No >>> first one.) >> >> Thema verfehlt. The question is: How does NUF(x) increase from 0 to >> more? There is a point where NUF is 0 and then it increases. How? > The same as the sign function. No, ℵo finite intervals do not fit between [0, 1] and (0, 1]. The sign function fits. > There simply is no such "point", as > there is no least positive number. The distances between unit > fractions get infinitely small. They remain finite in every case. Regards, WM