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A comment on ‘Infinitesimal,’ a Look at a 16th-Century Math Battle.

Re:‘Infinitesimal,’ a Look at a 16th-Century Math Battle by ciot1CDM on Monday January 18, 2016 @10:45PM (#10928748)
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)
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Re:‘Infinitesimal,’ a Look at a 16th-Century Math Battle by igravious on Tuesday January 19, 2016 @08:40AM (#10930616)
Should 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/ Part II Mathematics, 11 Real numbers, 11.6 The surreal numbers

[1] https://en.wikipedia.org/wiki/Surreal_number

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