Path: ...!news.mixmin.net!weretis.net!feeder8.news.weretis.net!reader5.news.weretis.net!news.solani.org!.POSTED!not-for-mail From: WM Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? Date: Wed, 2 Oct 2024 13:54:42 +0200 Message-ID: References: <298dcb6f-5f58-48b6-80e3-34260bf721f8@att.net> <283c426f-ab1c-4ef0-a06c-1bf7d28a2cfa@att.net> <6b50a171-8127-4ce6-9bd3-2dc213638e9b@att.net> <519db81b-4a4d-417d-8cd2-7fef5a342efd@att.net> <6704347e-2f99-40f2-887f-de93f6fdd659@tha.de> <8b3e744d-3419-40c3-a7c6-fe59edd528a9@tha.de> <851e9929-8ab7-49d1-b478-e65c61fba2e3@att.net> <78a0f795-f1c0-4ba5-90f9-acf667968011@att.net> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Wed, 2 Oct 2024 11:54:41 -0000 (UTC) Injection-Info: solani.org; logging-data="1100723"; mail-complaints-to="abuse@news.solani.org" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:Jdg5wk1lI9XZthVx4aw0Wjp+MKc= Content-Language: en-US X-User-ID: eJwFwYEBwDAEBMCV9MNjHCT2H6F3dvhxXGlUW1s2+MGDiWBJTAu6W+EtY8CLWivKpIJ17jRzr798d/2W/jsLFcM= In-Reply-To: Bytes: 2459 Lines: 18 On 02.10.2024 13:30, FromTheRafters wrote: > WM pretended : >> No. ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 does not prove that n+1 is a natural >> number. Note the infinite sequence >> 1, 2, 3, ..., ω-2, ω-1, ω. > > Omega minus one or two is undefined Yes in so far as these natural numbers are dark and cannot be reached by a FISON. > and n plus one closure is axiomatic. But it is in contradiction with NUF(x) passing 1. Do you understand that NUF(x) can nowhere increase by more than 1? Regards, WM