> According to ZFC, a function is a set whose members are pairs, such that no two different pairs have the same first element.

Can you cite where did you get this?

As I have said a few times now, you should read any first course in set theory. I’m quoting my third-year notes from Cambridge there, but essentially every intro to set theory will say the same. (I’m sure someone will find a single counterexample that does it somehow differently.)

Formally, a function f is a relation between sets A and B such that, for all x in A and u,v in B, f(x) = u and f(x) = v implies u = v.

It's just a definition. Authority is, as the parent suggests, any introduction to set theory.

The guy's remarkable response makes clear that he's a clueless troll.

> Formally, a function f is a relation

discussion was if zfc has functions at all, not sure why you put relation here.