Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: Andy Walker <anw@cuboid.co.uk>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Tue, 8 Apr 2025 20:10:58 +0100
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On 08/04/2025 18:00, Mr Flibble wrote:
> It is correct to say that infinitesimals don't exist:

	It's correct in standard analysis, because it's an axiom.  It's
not correct in number systems that have infinitesimals [and therefore
do not have the Archimedean axiom].

>							there is always a
> positive real number smaller than any candidate positive infinitesimal --
> this is basic logic.

	Google for "non-standard analysis" and for "surreal" [other
search engines are available].  Be warned that, at least the last time
I looked, Wiki is, as so often with maths topics, remarkably opaque for
non-mathematicians seeking enlightenment;  there are more user-friendly
introductions out there.  No, I'm not going to recommend one, it's a
matter of personal taste.

-- 
Andy Walker, Nottingham.
    Andy's music pages: www.cuboid.me.uk/andy/Music
    Composer of the day: www.cuboid.me.uk/andy/Music/Composers/Chwatal