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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: "Chris M. Thomasson" Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Date: Tue, 29 Oct 2024 15:16:50 -0700 Organization: A noiseless patient Spider Lines: 22 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> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Tue, 29 Oct 2024 23:16:51 +0100 (CET) Injection-Info: dont-email.me; posting-host="09272f6de4c78f3ebf892cfc59a706c2"; logging-data="1827986"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19Pi41aZ+j9s008pDw2yIVlcboE25N0+yE=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:fSIsWIRPg9u9jly00GeHsts86IY= In-Reply-To: Content-Language: en-US Bytes: 2993 On 10/29/2024 4:55 AM, joes wrote: > Am Tue, 29 Oct 2024 09:36:27 +0100 schrieb WM: >> On 29.10.2024 00:58, Richard Damon wrote: >>> On 10/28/24 3:42 PM, WM wrote: >> >>>> I mean that there are unit fractions. None is below zero. >>>> Mathematics proves that never more than one is at any point. >>> Which doesn't mean there must be a first, as they aproach an >>> accumulation point where the density becomes infinite. >> Their density is bounded by uncountably many points between every pair >> of consecutive unit fractions: >> The density is one point over uncountably many points, that is rather >> precisely 0. > So not bounded at all. > >>> Something which can't happen your world of finite logic, but does when >>> the logic can handle infinities. >> Where does the density surpass 1/10? Can you find this point? > How do you define the density at a point? > You need two points to get a difference that is non zero.