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Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: WM <wolfgang.mueckenheim@tha.de> Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? Date: Fri, 13 Sep 2024 20:05:59 +0200 Organization: A noiseless patient Spider Lines: 24 Message-ID: <vc1uu8$u3ec$9@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> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 13 Sep 2024 20:06:00 +0200 (CEST) Injection-Info: dont-email.me; posting-host="d45c0c2404748b6f9889e48002be3555"; logging-data="986572"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/o+BKeOcCHiHRUEx4NzVYGKy0uqPpXzok=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:PosU9WtZI+6lXR+eVodHIbhdHvk= In-Reply-To: <4faa63d0ff8c163f01a38736aeb5732184218a29@i2pn2.org> Content-Language: en-US Bytes: 2527 On 13.09.2024 17:52, Richard Damon wrote: > On 9/13/24 11:41 AM, WM wrote: >> Between [0, 1] and (0, 1] there is nothing, there is not a spot or >> point of the interval. >> > But that doesn't mean there is a lowest most point in (0, 1] as any > point you might want to call it will have another point between it and 0. I will not call any point but consider all points. There is no point smaller than all points in the open interval but a smallest one. Only 0 is smaller than all. > > Note, I said between the point your THINK is the first, there is no such > point, and thus you are agreeing to that fact. > > You can only have a first point in the open interval if the interval has > only a finite number of points, 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. Regards, WM