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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!i2pn.org!i2pn2.org!.POSTED!not-for-mail From: Richard Damon Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? Date: Fri, 6 Sep 2024 22:01:16 -0400 Organization: i2pn2 (i2pn.org) Message-ID: <6ae452e9b268b5b4c1867d9a7ca9fc023ecec9ef@i2pn2.org> References: <0da78c91e9bc2e4dc5de13bd16e4037ceb8bdfd4@i2pn2.org> <5d8b4ac0-3060-40df-8534-3e04bb77c12d@att.net> <7e1e3f62-1fba-4484-8e34-6ff8f1e54625@att.net> <06ee7920-eff2-4687-be98-67a89b301c93@att.net> <38ypmjbnu3EfnKYR4tSIu-WavbA@jntp> <34e11216-439f-4b11-bdff-1a252ac98f8f@att.net> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 7 Sep 2024 02:01:16 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="1049104"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird In-Reply-To: Content-Language: en-US X-Spam-Checker-Version: SpamAssassin 4.0.0 Bytes: 2311 Lines: 24 On 9/6/24 8:22 AM, WM wrote: > On 06.09.2024 00:36, Python wrote: >> Le 05/09/2024 à 22:44, crank Wolfgang Mückenheim, aka WM a écrit : > >>> >>> You are mistaken. I do not conclude the latter from the former. I >>> conclude the latter from the fact that NUF(0) = 0 and NUF(x>0) > 0 >>> and never, at no x, NUF can increase by more than 1. >> >> What the Hell could mean "to increase at an x" ? > > Example: The function f(x) = [x] increases at every x ∈ ℕ by 1. > The function NUF(x) increases at every x = unit fraction 1/n by 1. > It does not increase at 0 because 0 is not a unit fraction. > > Regards, WM Except that is can't because there is no "smallest" unit fraction to count from. Thus, either NUF(x) increases at some sub-finite values, or it doesn't exists. Sorry, you just don't understand that you need to show existance and not just presume it.