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Mark_Hanlon comments on Trust in Math - Less Wrong

14 Post author: Eliezer_Yudkowsky 15 January 2008 04:25AM

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Comment author: Mark_Hanlon 07 March 2008 09:02:31AM 0 points [-]

The discussion on this site seems to have many strands, but concerning Calculus - I was trying to figure it out for years and then came across smooth infinitesimal analysis. This is a version of analysis based on microstraightness and nilsquare infinitesimals. It reduces differential calculus to simple algebra, it does not lead to contradictions (such as the Banach-Tarski paradox), it facilitates physical derivations based on microadditivity, and it does not employ the dubious 'taking the standard part' trick of non-standard analysis (which is just Limit theory in disguise). The best book on the subject is A Primer of Infinitesimal Analysis by J L Bell.