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Path: ...!news.nobody.at!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? Date: Mon, 7 Oct 2024 12:57:01 -0700 Organization: A noiseless patient Spider Lines: 33 Message-ID: <ve1eee$1r206$4@dont-email.me> References: <vb4rde$22fb4$2@solani.org> <vdckd8$1tg01$1@dont-email.me> <vdefaq$29746$4@dont-email.me> <c23e4e3d9dfa7eade32142279e48303fe9f65539@i2pn2.org> <vdhc48$2qovo$2@dont-email.me> <461bf21a7f094701b936484f17bd3d68211fcf81@i2pn2.org> <vdjcg0$11itj$2@solani.org> <5086a1e540cdfb8fd979d8eca95ab8123166bf54@i2pn2.org> <vdmo3e$3r2lg$1@dont-email.me> <63b03cafeddb7c5485f1a863d629f56dd10c5bc1@i2pn2.org> <8d9d2296-ea12-4aa1-9e62-03828b3e516e@tha.de> <d0e0bd47dfb0b199c64b4e05fe17315c6750471d@i2pn2.org> <vdp228$96hv$1@dont-email.me> <vdpcja$alvo$5@dont-email.me> <95c4443902896e8ec4c5a99289332800ee56d33b@i2pn2.org> <bab0b508-82ea-42c1-bcb5-af42ea8ff230@tha.de> <87292fe4478728480baf991c7d2562fc7d372ecf@i2pn2.org> <vdrall$gag$1@solani.org> <075f62c7305fe7bf6aef0368b5c175d1fb37ba56@i2pn2.org> <vds29i$1ih6$4@solani.org> <08047fe749f5eb9e923344e444f7acaa419416e4@i2pn2.org> <vdu439$18f0b$1@dont-email.me> <de3e803094d2056522fc1adceeaeda76af5714a8@i2pn2.org> <ve07n4$1kopi$5@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 07 Oct 2024 21:57:02 +0200 (CEST) Injection-Info: dont-email.me; posting-host="1a2d03e8ed60e5a1a4eb0a20e66fceb4"; logging-data="1935366"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19/2dWoJGPHktO7evT9L9z0+OLfI30HMU8=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:F/Fq39PTPkllgHB4mCkpxqNOrZo= In-Reply-To: <ve07n4$1kopi$5@dont-email.me> Content-Language: en-US Bytes: 3025 On 10/7/2024 1:56 AM, WM wrote: > On 06.10.2024 19:11, Richard Damon wrote: >> On 10/6/24 9:42 AM, WM wrote: >>> On 06.10.2024 04:51, Richard Damon wrote: >>>> On 10/5/24 2:58 PM, WM wrote: >>> >>>>>>>>> Every point is a finite set. >>> >>>> The fact that we can keep doing that indefinitely, and never reach a >>>> point we can't continue, is proof that the concept of "next point" >>>> doesn't exist >>> >>> The concept of point however does exist. Every single point can be >>> found unless it is dark. >>> >> And every single point that exists can be found, and that includes >> every point on the "Number Line" > > Find the smallest unit fraction. Your brain? >> Except the "Unit Fractions" or the "Natural Numbers" those have gaps >> between the elements, with an "accumulation point" at 0 where the Unit >> Fractions become dense there. > > No. They nowhere become dense: ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 . > > Regards, WM >