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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: FromTheRafters Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Date: Wed, 30 Oct 2024 11:43:26 -0400 Organization: Peripheral Visions Lines: 15 Message-ID: References: <276fc9df-619b-4a10-b414-a04a74aa7378@att.net> <88e6a631-417a-4dd0-9443-a57116dcbd28@att.net> <7a1e34df-ffee-4d30-ae8c-2af5bcb1d932@att.net> <6a90a2e2-a4fa-4a8d-83e9-2e451fa8dd51@att.net> <0e5fb47d-60f7-42bb-beec-4a9661c807da@tha.de> Reply-To: erratic.howard@gmail.com MIME-Version: 1.0 Content-Type: text/plain; charset="utf-8"; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Wed, 30 Oct 2024 16:43:31 +0100 (CET) Injection-Info: dont-email.me; posting-host="fb33e71b2e0cf2f6ec1d1b566e43f886"; logging-data="2334697"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+aleyrjUV8QtoivdWLrLCPDoyPWMjCaVM=" Cancel-Lock: sha1:M9PC+Z3lSWfPl84e/7qh1UHtG5U= X-ICQ: 1701145376 X-Newsreader: MesNews/1.08.06.00-gb Bytes: 2472 on 10/30/2024, WM supposed : > On 30.10.2024 13:57, FromTheRafters wrote: >> WM explained : > >>> NUF(0) = 0, NUF(1) = ℵo. Therefore NUF must grow but cannot grow by more >>> than 1 at any point x of the real axis. >> >> The number of unit fractions less than x is always aleph_zero for positive >> x. > > Believe what you like without foundation. > If ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 is true, the NUF(x) grows in steps of not more > than 1. Wrong.