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Path: ...!eternal-september.org!feeder3.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? Date: Fri, 13 Sep 2024 19:20:25 +0200 Organization: A noiseless patient Spider Lines: 24 Message-ID: <vc1s8p$u3ec$8@dont-email.me> References: <vb4rde$22fb4$2@solani.org> <vbnuqq$2it4a$2@dont-email.me> <vbp9dk$2u3sh$1@dont-email.me> <vbq4ve$31fu6$10@dont-email.me> <fd09e9afa6b0c3041b90c5d788681bb2c92f9d2e@i2pn2.org> <vbs9v8$3l368$3@dont-email.me> <405557f7289631d63264c712d137244c940b9926@i2pn2.org> <vbsroa$3mvi7$2@dont-email.me> <vbt0fs$3pr1d$1@dont-email.me> <vbt15n$3qapk$1@dont-email.me> <btbO__HYVIMPfoOcmXp4_whV8-8@jntp> <vbums6$8kdn$1@dont-email.me> <vbv9i7$bpjh$2@dont-email.me> <acd6afe7-5de7-46a9-9438-8c8463fcd689@att.net> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 13 Sep 2024 19:20:25 +0200 (CEST) Injection-Info: dont-email.me; posting-host="d45c0c2404748b6f9889e48002be3555"; logging-data="986572"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19P5gBncttMjJ8EXXE/Pvf8U0dHyuTGyuI=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:ReSJFHsvK+OxmwfX++xzuF+d8Kg= In-Reply-To: <acd6afe7-5de7-46a9-9438-8c8463fcd689@att.net> Content-Language: en-US Bytes: 2221 On 12.09.2024 22:54, Jim Burns wrote: > On 9/12/2024 1:48 PM, WM wrote: >> On 12.09.2024 14:29, FromTheRafters wrote: >>> After serious thinking WM wrote : > >>>> But the endpoints of open intervals >>>> will remain dark forever. >>> >>> Open intervals simply don't contain endpoints, >>> dark or otherwise. >> >> You simply don't know about them. > > The boundary ∂A of set A is not a result of understanding points. Fact is that the real axis is nothing but its points. There is no gap. Every point has a next point but next to defined points are dark points. Next to every defined points there are ℵo dark points. This configuration cannot be changed. Regards, WM