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Path: ...!news.mixmin.net!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: Tue, 24 Sep 2024 21:35:23 +0200 Organization: A noiseless patient Spider Lines: 12 Message-ID: <vcv49q$3a5lv$9@dont-email.me> References: <vb4rde$22fb4$2@solani.org> <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> <c94d6140f000f75c5e95e1acc785ebff9894a18b@i2pn2.org> <vc7dk3$2b1g9$2@dont-email.me> <1aabd037-86bc-47bd-b402-f6b29c5c33e4@att.net> <vcehl6$2boc$3@dont-email.me> <f1d14b16-2c12-4cfb-b7f5-c58cc5724f94@att.net> <vcguvh$hi5j$1@dont-email.me> <b7eb4682-30db-4b37-90b4-0135e995cfc1@att.net> <vckekf$1709o$1@dont-email.me> <298dcb6f-5f58-48b6-80e3-34260bf721f8@att.net> <vcn8n8$1nfqa$1@dont-email.me> <283c426f-ab1c-4ef0-a06c-1bf7d28a2cfa@att.net> <vcpo5e$29qe5$1@dont-email.me> <6b50a171-8127-4ce6-9bd3-2dc213638e9b@att.net> <vcroj3$2nfvb$2@dont-email.me> <5e416e2d8ff7fcda1ba95f4c2f70d95b4698e838@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 24 Sep 2024 21:35:22 +0200 (CEST) Injection-Info: dont-email.me; posting-host="ce953f4ea89503f937d5933f72635f41"; logging-data="3479231"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18X7WFKYJebE6fLqAk9FxTLeFxLIPOz51Q=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:hKY4UdKW+ZREG/FnsfkTwGq0Aqc= In-Reply-To: <5e416e2d8ff7fcda1ba95f4c2f70d95b4698e838@i2pn2.org> Content-Language: en-US Bytes: 2423 On 24.09.2024 00:53, Richard Damon wrote: > On 9/23/24 8:57 AM, WM wrote: >> Yes. Therefore the smallest unit fraction must be dark. > > Which is something that doesn't exist. The function NUF(0) increases. ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 proves that it can gain only one unit fraction at any point x ∈ ℝ, hence NUF has to pass the value 1. Regards, WM