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Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: FromTheRafters <FTR@nomail.afraid.org> Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? Date: Fri, 27 Sep 2024 18:08:32 -0400 Organization: Peripheral Visions Lines: 14 Message-ID: <vd7ad6$sv60$1@dont-email.me> References: <vb4rde$22fb4$2@solani.org> <c94d6140f000f75c5e95e1acc785ebff9894a18b@i2pn2.org> <vc58cf$1o4dp$3@dont-email.me> <87jzfchnxc.fsf@bsb.me.uk> <vc7d61$2b1ga$1@dont-email.me> <4b617ec8573746a45483060acdd082653f14fda5@i2pn2.org> <vcehvl$2bop$1@dont-email.me> <vcfa23$67rd$3@dont-email.me> <vcfecj$6tlb$1@dont-email.me> <vch6v4$ip4a$1@dont-email.me> <vcht5k$mane$3@dont-email.me> <vci45p$n9ue$1@dont-email.me> <vckf64$1709n$5@dont-email.me> <c35b04a7d6ec19c5db1f9c5aba592f2614e09c9d@i2pn2.org> <890ae313-aa9b-4f49-a53a-2374c9957f01@tha.de> <2555906859e8d5836476a38f4fc437a67872f331@i2pn2.org> <vcp626$278um$5@dont-email.me> <534e5cd6b7a01203c28113337f108c745e57c6ae@i2pn2.org> <380cad54-83a7-4f20-976e-01d810d66c0a@att.net> <vcv4om$3a5lv$11@dont-email.me> <841bf27c18dffdc4ce0ea4d6392ccdfea2cef821@i2pn2.org> <vd19tt$3njbp$2@dont-email.me> <ac38f4a3b6d76f28c3acfec07c223f7a602b34f3@i2pn2.org> <vd1f6u$3od5s$6@dont-email.me> <f347fb8c-c754-4b7e-8e2e-b62135a9d351@tha.de> Reply-To: erratic.howard@gmail.com MIME-Version: 1.0 Content-Type: text/plain; charset="utf-8"; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 28 Sep 2024 00:08:39 +0200 (CEST) Injection-Info: dont-email.me; posting-host="2a2b1f78a5af67850fe4c3adde528787"; logging-data="949440"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/hxLhI/q0sG2rsHVPeniPcp3yUCBN8uVo=" Cancel-Lock: sha1:oGi1qn2BzBjqpc2C/8DB+Dx+OAU= X-Newsreader: MesNews/1.08.06.00-gb X-ICQ: 1701145376 Bytes: 2448 WM presented the following explanation : > On 25.09.2024 18:53, Moebius wrote: >>>>> On 9/24/24 3:43 PM, WM wrote: >>>> >>>>>> I think that [the] mathematics of fractions is correct. >>>>>> It contains ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 from which follows that never >>>>>> two different5 fractions sit upon each other. From NUF(0) = 0 the >>>>>> [existence of the] smallest unit fraction follows immediately >> >> Proof? > > Between two unit fractions there is always a finite gap. How big?