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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: Mon, 21 Oct 2024 00:46:33 -0700 Organization: A noiseless patient Spider Lines: 42 Message-ID: <vf50sp$s1mq$1@dont-email.me> References: <vb4rde$22fb4$2@solani.org> <vbnuqq$2it4a$2@dont-email.me> <vbp9dk$2u3sh$1@dont-email.me> <vbq4ve$31fu6$10@dont-email.me> <fd09e9afa6b0c3041b90c5d788681bb2c92f9d2e@i2pn2.org> <vbs9v8$3l368$3@dont-email.me> <405557f7289631d63264c712d137244c940b9926@i2pn2.org> <vbsroa$3mvi7$2@dont-email.me> <vbt0fs$3pr1d$1@dont-email.me> <vbt15n$3qapk$1@dont-email.me> <btbO__HYVIMPfoOcmXp4_whV8-8@jntp> <vbums6$8kdn$1@dont-email.me> <vbv9i7$bpjh$2@dont-email.me> <13c08e96ad635f8142b38d89863a80caf17a32a8@i2pn2.org> <vc1mfe$u3ec$2@dont-email.me> <4faa63d0ff8c163f01a38736aeb5732184218a29@i2pn2.org> <vc1uu8$u3ec$9@dont-email.me> <vc2gfb$130uk$1@dont-email.me> <vc44uu$1gc40$1@dont-email.me> <vc4h7q$1jd49$1@dont-email.me> <vc57ns$1o4dp$2@dont-email.me> <vc58go$1of9t$1@dont-email.me> <vc594g$1o4dp$4@dont-email.me> <vc5gfp$1tonu$1@dont-email.me> <vc5o7d$1vr09$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Mon, 21 Oct 2024 09:46:34 +0200 (CEST) Injection-Info: dont-email.me; posting-host="c770b3133348e91147f2be2370fb578a"; logging-data="919258"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19Z0lIA+1Ora8xQitdsexibHE0xFnx7b0k=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:bep+p5hG63TlX2gC40iZUD86Z+8= In-Reply-To: <vc5o7d$1vr09$1@dont-email.me> Content-Language: en-US Bytes: 3286 On 9/14/2024 9:35 PM, Chris M. Thomasson wrote: > On 9/14/2024 7:23 PM, Moebius wrote: >> Am 15.09.2024 um 02:18 schrieb Chris M. Thomasson: >>> On 9/14/2024 5:07 PM, Moebius wrote: >>>> Am 15.09.2024 um 01:54 schrieb Chris M. Thomasson: >>>>> On 9/14/2024 10:30 AM, FromTheRafters wrote: >>>>>> WM presented the following explanation : >>>>>>> On 14.09.2024 01:05, FromTheRafters wrote: >>>>>>>> WM explained : >>>>>>> >>>>>>>>> No, that is your big mistake. In the interval [0, 1] there is a >>>>>>>>> point next to 0 and a point next to 1, and infinitely many are >>>>>>>>> beteen them. >>>>>>>> >>>>>>>> Define 'next [to]' in this context. >>>>>>> >>>>>>> Two points are next to each other means that no point is between >>>>>>> them. >>>>>> >>>>>> So which point is next to zero. Is it rational, or is it >>>>>> irrational? In either case it is greater than zero and there is >>>>>> again more room for an even closer number. >>>> >>>> If r e IR, r > 0, then 0 < r/2 < r. >>>> >>>> Hence there is no real number > 0 "next to 0". >>>> >>>>> WM says .00001 is next to zero... Ahhh shit, what about .000001? >>> >>> .(0)1 is close to zero? ;^D >> >> Close, but no cigar. >> >> After all, 0.(0)01 is closer. :-P > > Indeed! ;^D ..(0)1 says its the closest to zero. ..(0)01 says that little shit is all hype! ;^) Like a comic strip.