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Path: ...!3.eu.feeder.erje.net!feeder.erje.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Python <python@invalid.org> Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? Date: Sun, 8 Sep 2024 22:34:01 +0200 Organization: CCCP Lines: 24 Message-ID: <vbl1nq$21t3j$3@dont-email.me> References: <vb4rde$22fb4$2@solani.org> <0da78c91e9bc2e4dc5de13bd16e4037ceb8bdfd4@i2pn2.org> <vb57lf$2vud1$1@dont-email.me> <5d8b4ac0-3060-40df-8534-3e04bb77c12d@att.net> <vb6o0r$3a4m1$2@dont-email.me> <7e1e3f62-1fba-4484-8e34-6ff8f1e54625@att.net> <vbabbm$24a94$1@solani.org> <06ee7920-eff2-4687-be98-67a89b301c93@att.net> <38ypmjbnu3EfnKYR4tSIu-WavbA@jntp> <34e11216-439f-4b11-bdff-1a252ac98f8f@att.net> <vbd56i$fqa0$1@dont-email.me> <vbdbq3$gdoe$2@dont-email.me> <vbes57$qdqo$2@dont-email.me> <27b3b5e088d82d4475c68a64f50a4bccac9c6f29@i2pn2.org> <vbesjo$27gfe$1@solani.org> <vbf0s9$qp1j$3@dont-email.me> <vbfpf5$utdu$2@dont-email.me> <vbh5qe$19a45$1@dont-email.me> <vbhdf6$1btm1$1@dont-email.me> <vbhffg$1bi3l$3@dont-email.me> <035b16b56a204dfe5e561b3cfe03238167dba39a@i2pn2.org> <vbhiv7$1bi3k$1@dont-email.me> <vbhmj4$1cg6l$4@dont-email.me> <vbkttc$20uoj$3@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 08 Sep 2024 22:34:02 +0200 (CEST) Injection-Info: dont-email.me; posting-host="819bf80071f695903b06caff553dc477"; logging-data="2159731"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+cVET2IHisxlfHOTCGDXmv" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:s6LXTGIO3UgTnJlFVNJuUNoOVsU= Content-Language: en-US In-Reply-To: <vbkttc$20uoj$3@dont-email.me> Bytes: 2589 Le 08/09/2024 à 21:28, Crank Mückenheim, aka WM a écrit : > On 07.09.2024 16:05, Python wrote: >> Le 07/09/2024 à 15:03, WM a écrit : > >>> Stop that nonsense. ℵo unit fractions cannot fit into every interval >>> (0, x). >> >> Of course they can. > > Select any gap between one of the first ℵo unit fractions and its > neighbour. Call its size x. x = 1/k - 1/(k+1) = 1/[k*(k+1)] > 0 > Then ℵo unit fractions cannot fit into the > interval (0, x), independent of the actual size. It can and it does : { 1/p : p > k*(k+1) } has cardinal ℵo, contains only unit fractions, and is a subset of (0, x) Ask one of your "students" if you don't understand, crank.