[carbotaniuman]

Does the functional equality being impossible to determine thing work for math problems? I know it works for computable functions, but math functions are pure and total so it seems easier.

[chongli]

Math functions are not total, in general. Computable functions are a subclass of all functions, so lots of functions are not computable.

Purity doesn't apply to functions, it applies to algorithms which compute functions. In software parlance the terms are often conflated but they are not equivalent. The algorithm which computes a function is in general not unique.

[xigoi]

The problem is that what you’re comparing are not functions, but representations of functions.

[kccqzy]

Just determining the equality of two real numbers is difficult.