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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: Does the number of nines =?UTF-8?Q?increase=3F?= References: Newsgroups: sci.math JNTP-HashClient: ul5WZxHrIGYEZWNs2oEEFFq-uH0 JNTP-ThreadID: 0JbXgoRqYUfKvvWhEBWZVJgnda4 JNTP-Uri: http://news2.nemoweb.net/?DataID=brLiXHwFSh6sqVSqbgI3CvYPP0M@jntp User-Agent: Nemo/0.999a JNTP-OriginServer: news2.nemoweb.net Date: Mon, 08 Jul 24 20:11:45 +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="25d5a506365fc8262443ce1bd287e5d0233c1bef"; logging-data="2024-07-08T20:11:45Z/8939257"; 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: 2826 Lines: 40 Le 08/07/2024 à 16:35, Moebius a écrit : > Am 08.07.2024 um 16:12 schrieb WM: >> Le 08/07/2024 à 04:52, Moebius a écrit : >> >>> (4) Es gilt also IN DER MENGENLEHRE für alle x e IR, x > 0: |{m e {1/n >>> : n e IN} : m <= x}| = aleph_0. >>> >>> (5) Mit der Definition NUF(x) := |{m e {1/n : n e IN} : m <= x}| folgt >>> also für alle x e IR, x > 0: NUF(x) = aleph_0. >> >> ℵo unit fractions occupy at least ℵo different points on the positive >> real axis. > > Nicht nur "at least", sondern "genau" There is no precision, no "genau" with ℵo. > >> Hence NUF(x) = ℵo cannot be true for x less than ℵo points, that is for >> a set of ℵo positive x. > > Huh?! You cannot think so far? What a pity. > > NUF(x) = ℵo ist für alle x e IR, x > 0 wahr. Not for the first ℵo points and their intervals required that the number of unit fractions can grow to ℵo. > Auch in diesem Fall gilt: NUF(0) = 0 und für alle x e IR, x > 0: NUF(x) > = aleph_0. > > Das ist alles ziemlich trivial. You cannot draw the conclusion: If X unit fractions occupy X points, then there cannot exist more than X unit fractions at the first X points. Ob alle Mathematiker zu blöde sind, um das zu verstehen? Gruß, WM