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Path: ...!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: Fri, 13 Sep 2024 12:31:47 -0700 Organization: A noiseless patient Spider Lines: 30 Message-ID: <vc23v3$10sij$1@dont-email.me> References: <vb4rde$22fb4$2@solani.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> <vbmi4b$2ce0a$1@dont-email.me> <vbn0tb$2d8fc$6@dont-email.me> <vbn3eb$2em18$4@dont-email.me> <ddcc775f8a3f832edadc6be01570b9fbf5c3ab4d@i2pn2.org> <vbnh3r$2gn74$4@dont-email.me> <9498e0c982f3e2ec8939341156ba52b4503c220d@i2pn2.org> <vbprfs$31fu6$4@dont-email.me> <1ddeedeb2c3985c15ce5664ad0fa707611a0514f@i2pn2.org> <vbs9s3$3l368$2@dont-email.me> <405d4f4a-ea61-438e-ac8f-4fcbc8927661@att.net> <7aee47eb-f2e3-4ae2-8981-b50e47f2768f@tha.de> <6280fabd-99e6-4836-8597-760f33d652c1@att.net> <vbujuc$7oto$1@dont-email.me> <40cb58f8-81c6-452f-bae4-65d50dc6ab76@att.net> <vc1ot5$u3ec$6@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 13 Sep 2024 21:31:48 +0200 (CEST) Injection-Info: dont-email.me; posting-host="32e5295bf326f2d283bb6f124540c159"; logging-data="1077843"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/ZVdG+X92cpdqA4Mn1ngWRYRGrO2/7fi8=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:cDnLUHehH2rleiCIRiKGuXUzXBI= In-Reply-To: <vc1ot5$u3ec$6@dont-email.me> Content-Language: en-US Bytes: 2987 On 9/13/2024 9:23 AM, WM wrote: > On 12.09.2024 21:12, Jim Burns wrote: >> On 9/12/2024 7:39 AM, WM wrote: > > >> ⎛ Expecting infinity to be unsurprising >> ⎜ is like >> ⎜ traveling to Outer Mongolia and >> ⎝ expecting everyone there to speak perfect German. > > Expecting infinity to obey logic is justified. >> >> Infinity is foreign. >> Foreign isn't uninvestigatable, > > I investigate it. I am sure that at every finite step Bob remains. And > there are no other steps, even if there are infinitely many. >>> Nevertheless (0,1] has a smallest point. >>> It is dark. >>> Where no point is, there is no interval. >>> Interval-ends without points are matheology. >> >> "Obvious" has devolved into gibberish. > > The real axis has no gaps, not even a single one at the end of (0, 1] > after zero. Real numbers are dense. Keep in mind that every unit fraction is a real, but not all reals are unit fractions... :^)