what are your favorite infinitesimals?
i'd really like a simple system of infinitesimals that feels intuitive for derivatives AND integrals
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What do you mean a system? What’s systematic about them? Like axiomatization of epsilon-delta operations?
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i mean like a specific formalism (ideally one that can fade into the background once learned)
the dual numbers are a good example, you just make up a number e such that e * e = 0
then you can differentiate f(x) by just evaluating (f(x+e)-f(x))/e
(fun thing to try out)
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another "system" would be non-standard analysis
this is where you pretend there's a number H that's like infinity but still a natural number, and then you can use 1/H as your infinitesimal
this one makes integrals nice, since you're just adding up H slices of width 1/H
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