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Path: ...!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? Date: Wed, 30 Oct 2024 12:57:31 -0700 Organization: A noiseless patient Spider Lines: 15 Message-ID: <vfu33c$29df4$2@dont-email.me> References: <vb4rde$22fb4$2@solani.org> <vfsmqr$207gj$6@dont-email.me> <vft9lf$25hsa$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Wed, 30 Oct 2024 20:57:32 +0100 (CET) Injection-Info: dont-email.me; posting-host="455c24f95a17f59c8fbd0a2a00f2944a"; logging-data="2405860"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19vBdwMx1n6jbrR41iF9nx7d33rv8+syhI=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:KCfPB4TpHMfLOi37oy9w9ykqpIs= In-Reply-To: <vft9lf$25hsa$1@dont-email.me> Content-Language: en-US Bytes: 1579 On 10/30/2024 5:43 AM, Moebius wrote: > Am 30.10.2024 um 08:22 schrieb Chris M. Thomasson: >> On 9/2/2024 10:07 AM, WM wrote: > >>> How many [...] unit fractions are lessorequal than all unit >>> fractions? The correct answer is: > > Zero. > > Hint: There is no smallest unit fraction. > > Proof: If u is a unit fraction, then 1/(1/s + 1) is a unit fraction > which is smaller than u. qed 1/2 is the smallest. What about 1/(2+1) ? WM, ahhh what a shit.