Post #3832637
2026-05-26 03:25 UTC
@FishFace@ioc.exchange Thank you! IMO using infinitesimals to teach calculus is a terrible idea. Using them rigorously requires understanding VERY difficult and advanced mathematics. The epsilon-delta definition of limit is hard but requires no exotic ideas. Convergent sequences and Cauchy sequences, if needed, are a little easier.
Replies (1)
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@FishFace@ioc.exchange 2026-05-26 08:11
@spradlig@mathstodon.xyz I would guess you might mean "to teach analysis"? I have heard that using calculus (ie non rigorously) with infinitesimals as a technique, rather than a rigorous foundation, can be quite successful. Keisler's calculus textbook uses infinitesimals in this way - with what amounts to an axiomatic and intuitive development of infinitesimals in order to do calculus, saving their rigorous construction until the end. It's a bit like doing calculus and saving Dedekind Cuts for later :) Michal Katz has done research on this from a pedagogical perspective (although he is *very* committed to it - he's far from a neutral observer) which is quite interesting.