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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 10:07:41 -0400 Organization: Peripheral Visions Lines: 42 Message-ID: <vfo5rf$1178s$1@dont-email.me> References: <vb4rde$22fb4$2@solani.org> <vf66bb$125ku$1@dont-email.me> <08a00c75-bf8d-4f9c-816a-83b8517ca04e@att.net> <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> 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 15:07:44 +0100 (CET) Injection-Info: dont-email.me; posting-host="c02dc0ac18140c169f23ce4fbf1f6f03"; logging-data="1088796"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19lwPSs+i6l9Els7qnP5OjQYMNITG09IjY=" Cancel-Lock: sha1:xIutd923gTMUcn/i9BwvUty8zzk= X-Newsreader: MesNews/1.08.06.00-gb X-ICQ: 1701145376 Bytes: 3174 WM was thinking very hard : > On 27.10.2024 20:01, FromTheRafters wrote: >> WM pretended : >>> Am 27.10.2024 um 14:39 schrieb FromTheRafters: >>> >>>> If 'not defined' could be a proper subset of the naturals, then there >>>> would be a first such 'not defined' in that subset. Of course WM can't >>>> substantiate any of his wild claims. >>> >>> Proof: >> >> Blah blah blah. > > Very substantial. > > Proof: If infinity is actual, There need not be any distinction between infinity and your always finite but increasing sequence of sets. Infinite means not finite. > then all elements of the set of unit fractions exist. They do anyway. > The function NUF(x) = Number of Unit Fractions between 0 and x starts > with 0 at 0. Followed by a discontinuity. > 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. > 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 doesn't have to happen step by step as you envision it. > Of course x' and x'' are Blah blah blah.