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Path: ...!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: WM <wolfgang.mueckenheim@tha.de> Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Date: Mon, 28 Oct 2024 20:27:46 +0100 Organization: A noiseless patient Spider Lines: 34 Message-ID: <vfooji$14lcc$1@dont-email.me> References: <vb4rde$22fb4$2@solani.org> <vf526v$s8qs$2@dont-email.me> <vf56f2$svda$1@dont-email.me> <vf58pv$t8hc$2@dont-email.me> <5e5ccee7-0c98-4701-aeaa-4950a3ce2938@att.net> <vf66bb$125ku$1@dont-email.me> <08a00c75-bf8d-4f9c-816a-83b8517ca04e@att.net> <vf7mqj$1d3m4$2@dont-email.me> <062a0fa5-9a15-4649-8095-22c877af5ebf@att.net> <vf8itt$1hosd$2@dont-email.me> <b1e5a319-eaec-44d2-b961-f90bc241e7e6@att.net> <vf8r7k$1jnia$2@dont-email.me> <d316baa3-de5b-4644-86ff-beacad9df107@att.net> <vfd97u$2jtos$1@dont-email.me> <276fc9df-619b-4a10-b414-a04a74aa7378@att.net> <vfe5d5$2olom$1@dont-email.me> <88e6a631-417a-4dd0-9443-a57116dcbd28@att.net> <vfg07k$1chpe$1@solani.org> <7a1e34df-ffee-4d30-ae8c-2af5bcb1d932@att.net> <vfgil3$38pn6$1@dont-email.me> <6a90a2e2-a4fa-4a8d-83e9-2e451fa8dd51@att.net> <vfgqoc$39o4h$2@dont-email.me> <acd4aad3-9447-45a9-bafd-f8b93d781827@att.net> <vfj3v0$1e96h$2@solani.org> <e083912c-502b-4cf0-b05c-abbfa4c9f455@att.net> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 28 Oct 2024 20:27:46 +0100 (CET) Injection-Info: dont-email.me; posting-host="028c8f7ef7e0642f2efab9c9f9b9b737"; logging-data="1201548"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/k3miYlx+THozgnZlGe26b+h1h9asQx/w=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:KoLPl9+ZTVO/SKvA8raT4G9SEGY= Content-Language: en-US In-Reply-To: <e083912c-502b-4cf0-b05c-abbfa4c9f455@att.net> Bytes: 3060 On 28.10.2024 19:31, Jim Burns wrote: > On 10/26/2024 12:04 PM, WM wrote: >> No, you falsely assume that >> all natnumbers can be defined. > > I assume that > natural numbers are finite ordinals, and > > that a finite ordinal is predecessored or is 0 and > each of its priors is predecessored or is 0, and > > that an ordinal is successored and > a set of ordinals is minimummed or is {} That is irrelevant with respect to the fact that between every chosen unit fraction and zero there are ℵo unit fractions which cannot be chosen. After every definable Endsegment with |∩{E(1), E(2), ..., E(k)}| = ℵo there remain ℵo endsegments which cannot be defined. >> Try to define more unit fractions >> than remain undefined. > > 𝗖𝗹𝗮𝗶𝗺𝘀 exist which do not answer the question. > > Each rational can be given as a fraction. There remain ℵo endsegments which cannot be defined. Otherwise the definition of accumulation point was wrong. Regards, WM