Path: ...!weretis.net!feeder9.news.weretis.net!i2pn.org!i2pn2.org!.POSTED!not-for-mail From: joes Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Date: Wed, 9 Oct 2024 17:08:02 -0000 (UTC) Organization: i2pn2 (i2pn.org) Message-ID: References: <4bc3b086-247a-4547-89cc-1d47f502659d@tha.de> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Injection-Date: Wed, 9 Oct 2024 17:08:02 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="1283985"; 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: 3266 Lines: 43 Am Wed, 09 Oct 2024 14:48:17 +0200 schrieb WM: > On 08.10.2024 23:08, Alan Mackenzie wrote: >> WM wrote: >>> On 07.10.2024 18:11, Alan Mackenzie wrote: >>>> What I should have written (WM please take note) is: >> >>>> The idea of one countably infinite set being "bigger" than another >>>> countably infinite set is simply nonsense. >>> The idea is supported by the fact that set A as a superset of set B is >>> bigger than B. >> What do you mean by "bigger" as applied to two infinite sets when one >> of them is not a subset of the other? > That is not in every case defined. But here are some rules: > Not all infinite sets can be compared by size, but we can establish some > useful rules. [copypasta] That is a weakness of your notion of cardinality. How do you compare finite sets? >>> Simply nonsense is the claim that there are as many algebraic numbers >>> as prime numbers. >> It is not nonsense. The prime numbers can be put into 1-1 >> correspondence with the algebraic numbers, therefore there are exactly >> as many of each. > Nonsense. Only potential infinity is used. Never the main body is > applied. What "main body"? >>> For Cantor's enumeration of all fractions I have given a simple >>> disproof. >> Your "proofs" tend to be nonsense. > Theorem: If every endsegment has infinitely many numbers, then > infinitely many numbers are in all endsegments. > Proof: If not, then there would be at least one endsegment with less > numbers. I struggle to follow this illogic. Why should one segment have less numbers? > Note: The shrinking endsegments cannot acquire new numbers. Not necessary, they already contain as many as needed. -- 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.