Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: FromTheRafters Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? Date: Fri, 13 Sep 2024 19:05:08 -0400 Organization: Peripheral Visions Lines: 24 Message-ID: References: <405557f7289631d63264c712d137244c940b9926@i2pn2.org> <13c08e96ad635f8142b38d89863a80caf17a32a8@i2pn2.org> <4faa63d0ff8c163f01a38736aeb5732184218a29@i2pn2.org> Reply-To: erratic.howard@gmail.com MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-15"; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 14 Sep 2024 01:05:16 +0200 (CEST) Injection-Info: dont-email.me; posting-host="4cdda06936719fac9e1d1ac3c0d09690"; logging-data="1147860"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/Fu5UOhpRCqsHHSWwp53e1l6D3Slt8ZAI=" Cancel-Lock: sha1:OZNIJhF1cbUF1kfIg95DUzhvuzM= X-Newsreader: MesNews/1.08.06.00-gb X-ICQ: 1701145376 Bytes: 2569 WM explained : > On 13.09.2024 17:52, Richard Damon wrote: >> On 9/13/24 11:41 AM, WM wrote: > >>> Between [0, 1] and (0, 1] there is nothing, there is not a spot or point >>> of the interval. >>> >> But that doesn't mean there is a lowest most point in (0, 1] as any point >> you might want to call it will have another point between  it and 0. > > I will not call any point but consider all points. There is no point smaller > than all points in the open interval but a smallest one. Only 0 is smaller > than all. >> >> Note, I said between the point your THINK is the first, there is no such >> point, and thus you are agreeing to that fact. >> >> You can only have a first point in the open interval if the interval has >> only a finite number of points, > > No, that is your big mistake. In the interval [0, 1] there is a point next to > 0 and a point next to 1, and infinitely many are beteen them. Define 'next' in this context.