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: Fri, 4 Oct 2024 11:49:17 +0200 Organization: A noiseless patient Spider Lines: 16 Message-ID: References: <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: Fri, 04 Oct 2024 11:49:19 +0200 (CEST) Injection-Info: dont-email.me; posting-host="f4b38fa814833d08fac49dd116a99714"; logging-data="193458"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+47/zWf8Fz3a1YmselXB+Fs/d9dB2bzmo=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:vTLmmoTSW74VkD2+pkYBwxvmy4k= Content-Language: en-US In-Reply-To: Bytes: 2460 On 04.10.2024 10:22, Moebius wrote: > Am 04.10.2024 um 10:17 schrieb joes: >> Am Thu, 03 Oct 2024 20:20:52 +0200 schrieb WM: > >>> If all fractions are separated real points on the real axis, then there >>> must be a first one. > > Nope. > > Hint: The harmonic series is divergent [at least in mathematics]. Correct but irrelevant. The sum of all natural numbers is larger than ω. Nevertheless ω-1 is the last natural number. Regards, WM