Path: ...!news.misty.com!weretis.net!feeder9.news.weretis.net!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail From: joes Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? Date: Mon, 9 Sep 2024 15:49:16 -0000 (UTC) Organization: i2pn2 (i2pn.org) Message-ID: References: <06ee7920-eff2-4687-be98-67a89b301c93@att.net> <38ypmjbnu3EfnKYR4tSIu-WavbA@jntp> <34e11216-439f-4b11-bdff-1a252ac98f8f@att.net> <27b3b5e088d82d4475c68a64f50a4bccac9c6f29@i2pn2.org> <9eeba8a5041ce7ee48e5019d9e98d4ea38a1eb72@i2pn2.org> <89ed6d8de6c20d65e869d384181b642309f63bc4@i2pn2.org> <7a991922c09e309450ac278f884091dfe716cae3@i2pn2.org> <918c948309b4a74d0bc505a1c2f40a7868072f41@i2pn2.org> <4f9cb578fe0b0891c115fd21cbc25642f706b63a@i2pn2.org> <83d741b4-a0bc-42f3-a286-9d26d164ff66@tha.de> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Injection-Date: Mon, 9 Sep 2024 15:49:16 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="1409728"; mail-complaints-to="usenet@i2pn2.org"; posting-account="nS1KMHaUuWOnF/ukOJzx6Ssd8y16q9UPs1GZ+I3D0CM"; User-Agent: Pan/0.145 (Duplicitous mercenary valetism; d7e168a git.gnome.org/pan2) X-Spam-Checker-Version: SpamAssassin 4.0.0 Bytes: 2681 Lines: 16 Am Mon, 09 Sep 2024 17:32:11 +0200 schrieb WM: > On 09.09.2024 17:15, joes wrote: >> Am Mon, 09 Sep 2024 16:53:32 +0200 schrieb WM: > >>> You claim that ℵo unit fractions are smaller than ANY x > 0. >> Yes. Not all the same ones of course. > My question concerns same unit fractions only. Do ℵo unit fractions > exist smaller than any x > 0? If not, how many same unit fractions exist > smaller than any x > 0? How many are smalleror equal than all unit > fractions? That is a different question (quantifier order). Of course no unit fraction is smaller than every other unit fraction. (I don’t understand the „same” question.) -- Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math: It is not guaranteed that n+1 exists for every n.