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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: WM <wolfgang.mueckenheim@tha.de> Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? Date: Mon, 9 Sep 2024 12:19:56 +0200 Organization: A noiseless patient Spider Lines: 26 Message-ID: <vbmi4b$2ce0a$1@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> <vbl1nq$21t3j$3@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 09 Sep 2024 12:19:56 +0200 (CEST) Injection-Info: dont-email.me; posting-host="9f237e696ac80d598d2ebb925ba28b52"; logging-data="2504714"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+Z7QNXT7lawJE04rueb09c5Sms0ti6zgk=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:z68oVqrvXNUkCgZ939rBkLBR52Q= Content-Language: en-US In-Reply-To: <vbl1nq$21t3j$3@dont-email.me> Bytes: 2666 On 08.09.2024 22:34, Python wrote: > 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 Nonsense. ℵo unit fractions cannot fit into one of the ℵo intervals between two of them. Regards, WM