Path: news.eternal-september.org!eternal-september.org!feeder3.eternal-september.org!news.szaf.org!news.karotte.org!news.space.net!news.muc.de!.POSTED.news.muc.de!not-for-mail From: Alan Mackenzie Newsgroups: sci.math Subject: Re: The non-existence of "dark numbers" Date: Tue, 18 Mar 2025 12:18:27 -0000 (UTC) Organization: muc.de e.V. Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Injection-Date: Tue, 18 Mar 2025 12:18:27 -0000 (UTC) Injection-Info: news.muc.de; posting-host="news.muc.de:2001:608:1000::2"; logging-data="78886"; mail-complaints-to="news-admin@muc.de" User-Agent: tin/2.6.4-20241224 ("Helmsdale") (FreeBSD/14.2-RELEASE-p1 (amd64)) WM wrote: > On 18.03.2025 10:56, FromTheRafters wrote: >> on 3/18/2025, WM supposed : >>> The set is ordered and if it is actually infinite, then all its=20 >>> elements are there and=C2=A0 do not appear from nothing but then it h= as a=20 >>> greatest element. >> Nope, it is a limit ordinal. > All elements of =E2=84=95 are there. That is the assumption. If no grea= test can=20 > be identified, then the reason are dark numbers. No, the reason is that there is no greatest element. "Dark numbers" do not exist, as has been proven in this thread. > Otherwise only potential infinity could solve the dilemma. There is no dilemma here. "Potential infinity" doesn't exist in modern mathematics. It was a blind alley the pioneers of set theory drove up. "Potential infinity" isn't a useful concept and isn't needed in mathematics. > Regards, WM --=20 Alan Mackenzie (Nuremberg, Germany).