Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: Andy Walker Newsgroups: comp.theory Subject: Re: Cantor Diagonal Proof Date: Tue, 8 Apr 2025 20:10:58 +0100 Organization: Not very much Lines: 22 Message-ID: References: <4DcJP.430046$dBr6.129536@fx04.ams4> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Tue, 08 Apr 2025 21:10:58 +0200 (CEST) Injection-Info: dont-email.me; posting-host="64901bbcb8a2ed2ef171308186d80d97"; logging-data="1920153"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/hLcm36PBBrINzM4bjlAZ7" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:NZ4PcP7IfUCwJFfF+sermVmoiUY= Content-Language: en-GB In-Reply-To: <4DcJP.430046$dBr6.129536@fx04.ams4> 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