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: ...!feeds.phibee-telecom.net!news.mixmin.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Moebius Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? Date: Tue, 10 Sep 2024 02:36:51 +0200 Organization: A noiseless patient Spider Lines: 14 Message-ID: References: <7e1e3f62-1fba-4484-8e34-6ff8f1e54625@att.net> <06ee7920-eff2-4687-be98-67a89b301c93@att.net> <38ypmjbnu3EfnKYR4tSIu-WavbA@jntp> <34e11216-439f-4b11-bdff-1a252ac98f8f@att.net> <27b3b5e088d82d4475c68a64f50a4bccac9c6f29@i2pn2.org> <9eeba8a5041ce7ee48e5019d9e98d4ea38a1eb72@i2pn2.org> <89ed6d8de6c20d65e869d384181b642309f63bc4@i2pn2.org> <937a4a53c27b209538bb77bfe8059a90cc70ee9e@i2pn2.org> Reply-To: invalid@example.invalid MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Tue, 10 Sep 2024 02:36:51 +0200 (CEST) Injection-Info: dont-email.me; posting-host="f04efbf94a3a01cd7b7f06f1c9ebdc98"; logging-data="2737279"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/8sb5IoXDFyzUFrw1/Cmxp" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:XAj4sDNl8KlIMRMdILMJAlBNe+4= Content-Language: de-DE In-Reply-To: Bytes: 2515 Am 10.09.2024 um 02:32 schrieb Moebius: > Am 10.09.2024 um 01:08 schrieb Chris M. Thomasson: > >> Take the gap between: >> >> 1/1 and 1/2. There are infinitely many unit fractions that are small >> enough to fit within that gap. > > Oh, really?! Could you name (just) o n e? :-) > > I mean ... a unit fraction u such that 1/2 < u < 1/1. :-o Hint, you see... 1/3 < 1/2 < 1/1. Actually, for each and every k e IN with k > 2: 1/k < 1/2 < 1/1.