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If you're interested in a modern rigorous treatment of the classical infinitesimal, check out "smooth infinitesimal analysis" (https://en.wikipedia.org/wiki/Smo
by ciot1CDM 11y ago
If you're interested in a modern rigorous treatment of the classical infinitesimal, check out "smooth infinitesimal analysis" (https://en.wikipedia.org/wiki/Smooth_infinitesimal_analysis https://en.wikipedia.org/wiki/Smooth_infinitesimal_analysis)
- igravious 11y agoShould have checked sooner for replies to my post, sorry! I actually posted the above review/link in the hope that somebody would mention nilpotent infinitesimals and smooth infinitesimal analysis. Interesting, in my opinion, is that homotopy type theory (HoTT)[0] has taken Conway's surreal numbers[1] approach. Given that I think HoTT is the correct _foundational_ tack and at the same time I also think that smooth infinitesimal analysis is the correct _calculus_ tack I'd very much like to see the two methods combined. [0] http://homotopytypetheory.org/book/ http://homotopytypetheory.org/book/ Part II Mathematics, 11 Real numbers, 11.6 The surreal numbers [1] https://en.wikipedia.org/wiki/Surreal_number https://en.wikipedia.org/wiki/Surreal_number