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: comp.theory Subject: Re: Cantor Diagonal Proof Date: Wed, 9 Apr 2025 16:17:37 -0000 (UTC) Organization: muc.de e.V. Message-ID: References: <4DcJP.430046$dBr6.129536@fx04.ams4> <875xjes23l.fsf@nosuchdomain.example.com> Injection-Date: Wed, 9 Apr 2025 16:17:37 -0000 (UTC) Injection-Info: news.muc.de; posting-host="news.muc.de:2001:608:1000::2"; logging-data="33147"; mail-complaints-to="news-admin@muc.de" User-Agent: tin/2.6.4-20241224 ("Helmsdale") (FreeBSD/14.2-RELEASE-p1 (amd64)) Mr Flibble wrote: > On Wed, 09 Apr 2025 14:11:54 +0000, Alan Mackenzie wrote: >> Mr Flibble wrote: >>> On Tue, 08 Apr 2025 15:46:54 -0700, Keith Thompson wrote: >> [ .... ] >>>> If you're interested in learning more, search for "surreal numbers" or >>>> "hyperreal numbers". If you're not, don't. >>> Surreal numbers are bullshit as they don't actually exist, logically >>> (as I have show). Bullshit can be internally consistent with itself. >> What exactly do you mean by a mathematical entity "not existing"? What >> is your test which partitions such entities into "existing" and >> "non-existing"? >>> /Flibble > Simple: things that make no logical sense don't exist: .... Surreal numbers do make logical sense. They form an ordered field which has the real numbers as a subfield. > .... logically a real number always has a number smaller than it .... Every stricly positive surreal number has a number smaller than it, too. > .... so trying to put a "surreal" infinitesimal on the same number line > as a "real" makes no logical sense: in fact I will go as far to say > that it is a category error. The surreal number line is not the real number line, so trying to put a surreal on the latter indeed makes no sense. It might even constitute a category error, as you suggest. That, however, has no bearing on the existence of surreal numbers. They don't create inconsistencies, hence do exist, and have been studied intensively. > /Flibble -- Alan Mackenzie (Nuremberg, Germany).