3 ms·

If you take x as a stand-in for a number, then df/dx simply makes no sense, df/d(5) is either nonsense or division by zero. Your approach doesn't seem to make m

If you take x as a stand-in for a number, then df/dx simply makes no sense, df/d(5) is either nonsense or division by zero. Your approach doesn't seem to make more sense out of Leibniz notation, unless I misunderstand what you mean by f(x) being an element of the range.

bmacho 3y ago
If you know a language with function types, then you can think of it as f : R -> R that is, f having a type signature as a function, and f(x) : R having a type signature of a float (or: being a float). And so on. I've been using this approach to type-check calculus equations. Unfortunately the article in the top comment [0] says that > Note that f means something different on the two sides of the equation! so the Leibniz notation might be more ad-hoc than I thought, and I can't just type-check them, actually have to reverse engineer the intent of the authors. I have to think about this. For example I remember someone giving me 3 exercises from Stewart calculus, and I gave 2 back that those equations don't even type-check, maybe there are some notation abuses I am not aware of. [0] https://mitp-content-server.mit.edu/books/content/sectbyfn/books_pres_0/9579/sicm_edition_2.zip/preface001.html https://mitp-content-server.mit.edu/books/content/sectbyfn/b...