CONFIRMED: infinitesimal calculus via Liebniz *is* closer to how I think than that they tried showing me in school.
Example: [text example found in a real-life book I’m reading backwards, “Mathematics 1001 : Absolutely Everything That Matters in Mathematics in 1001 Bite-Size Explanations”. The image is not from the book but I’ll link to that below]
Under : EXPONENTIATION: “The Exponentiation Function”
”
In short:
d
— (exp x) = exp x
dx
This says that the exponential function describes its own rate of change.
”
This way of looking at things brings time / rate of change *back* into even basic functions such as “2^3”.
(I also like Lagrange’s notation as it brings an index in)
In any event, this “way of thinking” allows an easy translation into imperative programming, a language + grammar I’m familiar with.
It takes time to do functions. By unrolling it like this not only can you see what even something like a basic exponent is doing, but you can also make other things happen while it’s doing it.
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