Sounds legit, infinity is singular and so is 0. I think one problem is also that division isn't the only mathematical operation which can produce dubious results. E.g. sqrt(x), arctan(x) which have multiple branches which is why there is often a separate arctan2(x, y) to select the correct branch. Oh well and then there's just addition which silently overflows in almost every programming language.

Without arbitrary precision numerics and functions which aren't explicit about corner cases it's always a simplification. However performance-/code-wise this is usually not feasible.