> So the type of the return value changes at asymptotes/limits (already) and thus that's not a pure function in terms of math. Plenty of functions are disconti

> So the type of the return value changes at asymptotes/limits (already) and thus that's not a pure function in terms of math. Plenty of functions are discontinuous. Almost all of them, in fact. (This isn't true constructively, but GP is clearly doing classical analysis.) > If a [math] function returns a more complex type signature instead of throwing a ZeroDivisionError (as Python core does) what is that then called? Is it differentiable or no, etc? Depends on the smooth structures you've imposed on the domain and codomain, which requires much more powerful types to represent than are available in any mainstream language I'm aware of. (You might be able to contort Haskell into something sort of close, but it wouldn't be simple.)