Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: WM 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: References: <405557f7289631d63264c712d137244c940b9926@i2pn2.org> 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: 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