Path: ...!news.mixmin.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: WM 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: References: <13c08e96ad635f8142b38d89863a80caf17a32a8@i2pn2.org> <4faa63d0ff8c163f01a38736aeb5732184218a29@i2pn2.org> <1aabd037-86bc-47bd-b402-f6b29c5c33e4@att.net> <298dcb6f-5f58-48b6-80e3-34260bf721f8@att.net> <283c426f-ab1c-4ef0-a06c-1bf7d28a2cfa@att.net> <6b50a171-8127-4ce6-9bd3-2dc213638e9b@att.net> <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