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Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: FromTheRafters <FTR@nomail.afraid.org> Newsgroups: sci.math Subject: Re: =?ISO-8859-15?Q?There_is_a_first/smallest_integer_(in_M=FCcke?= =?ISO-8859-15?Q?nland)?= Date: Wed, 17 Jul 2024 13:13:09 -0400 Organization: Peripheral Visions Lines: 15 Message-ID: <v78u39$1ubd0$1@dont-email.me> References: <v78aei$1qhrg$2@dont-email.me> <v78ho8$1rucd$1@dont-email.me> <hkTLLEKjGrtEv-QUxN7BX0GQq58@jntp> Reply-To: erratic.howard@gmail.com MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-15"; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Wed, 17 Jul 2024 19:13:14 +0200 (CEST) Injection-Info: dont-email.me; posting-host="03d7a5d40b3296705afef7ca976a13f6"; logging-data="2043296"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+PYgNUpKnMnUhMGi5nMiLip3gzDQVoDzg=" Cancel-Lock: sha1:or8D3JEk2aSD5mBc5Zkw5RYzFlk= X-ICQ: 1701145376 X-Newsreader: MesNews/1.08.06.00-gb Bytes: 1703 WM presented the following explanation : > Le 17/07/2024 à 15:42, FromTheRafters a écrit : >> Moebius presented the following explanation : >>> WM> All unit fractions are separated. Therefore there is a first one >>> >>> Moebius> All integers are separated. Therefore there is a first one [?] >>> >>> WM> This is true but difficult to understand. >> >> Perhaps, with professional counseling, > > you could explain how NUF(x) can increase from 0 to many more in one point > although all unit fractions are separated by finite distances? Sure, it jumps because of your stepwise function.