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Path: ...!eternal-september.org!feeder2.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? (infinitary) Date: Mon, 28 Oct 2024 16:51:18 -0400 Organization: Peripheral Visions Lines: 32 Message-ID: <vfotg8$15r9a$1@dont-email.me> References: <vb4rde$22fb4$2@solani.org> <vf7mqj$1d3m4$2@dont-email.me> <062a0fa5-9a15-4649-8095-22c877af5ebf@att.net> <vf8itt$1hosd$2@dont-email.me> <b1e5a319-eaec-44d2-b961-f90bc241e7e6@att.net> <vf8r7k$1jnia$2@dont-email.me> <d316baa3-de5b-4644-86ff-beacad9df107@att.net> <vfd97u$2jtos$1@dont-email.me> <276fc9df-619b-4a10-b414-a04a74aa7378@att.net> <vfe5d5$2olom$1@dont-email.me> <88e6a631-417a-4dd0-9443-a57116dcbd28@att.net> <vfg07k$1chpe$1@solani.org> <7a1e34df-ffee-4d30-ae8c-2af5bcb1d932@att.net> <vfgil3$38pn6$1@dont-email.me> <6a90a2e2-a4fa-4a8d-83e9-2e451fa8dd51@att.net> <vfgqoc$39o4h$2@dont-email.me> <acd4aad3-9447-45a9-bafd-f8b93d781827@att.net> <vfj3v0$1e96h$2@solani.org> <vfjg9h$3rjvp$2@dont-email.me> <vfkqlr$3fii$1@solani.org> <vfl8o7$3mnmt$4@i2pn2.org> <vflfq9$f82l$1@dont-email.me> <vflovl$1fpr2$3@solani.org> <vfm2m5$iasq$1@dont-email.me> <vfnmo3$ui6v$1@dont-email.me> <vfo5rf$1178s$1@dont-email.me> <vfoqqr$14lcc$2@dont-email.me> 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: Mon, 28 Oct 2024 21:51:21 +0100 (CET) Injection-Info: dont-email.me; posting-host="c02dc0ac18140c169f23ce4fbf1f6f03"; logging-data="1240362"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19ro/FozF87u1aDlM/AflynL7W5S9dEk/M=" Cancel-Lock: sha1:oRRz1IZSKiO+NiURrDejJC3e9AE= X-ICQ: 1701145376 X-Newsreader: MesNews/1.08.06.00-gb Bytes: 2937 WM explained : > On 28.10.2024 15:07, FromTheRafters wrote: >> WM was thinking very hard : > >>> The function NUF(x) = Number of Unit Fractions between 0 and x starts with >>> 0 at 0. >> >> Followed by a discontinuity. > > No. ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 holds everywhere. Not for n equal to zero. >>> After NUF(x') = 1 it cannot change to NUF(x'') = 2 without pausing for an >>> interval consisting of uncountably many real points. >> >> Your "Axiom of because I say so" is overworked. > > It is mathematics:>> The reason is this: ∀n ∈ ℕ: 1/n - 1/(n+1) > 0. >> >> Non sequitur. This is just the second part of your stepwise function. > > It holds everywhere if mathematics holds everywhere. > >> It doesn't have to happen step by step as you envision it. > > As mathematics dictates it. > > You have confessed: In order to maintain actual infinity without dark > numbers, you have to violate mathematics. Bull! Just another of your non sequiturs.