1. The problem statement, all variables and given/known data Two functions f and g are equal iff (a) f and g have the same domain, and (b) f(x) = g(x) for every x in the domain of f. Not actually hw, but I wanted to prove or at least see the elementary proof of this theorem. 2. Relevant equations just the formal function definition: A function f is a set of ordered pairs (x,y) [such that] no two of which have the same first member. y = f(x), customarily is used over (x,y) is an element of f 3. The attempt at a solution Alright, I just want to know if I'm over-simplifying here...but, Since f is a set of ordered pairs and g is a set of ordered pairs, for f = g we must have that every ordered pair in f is an ordered pair in g and every ordered pair in g is an ordered pair in f (subsets of one another). For f and g to be equal then, they must contain the same first members and thus the same domain. And then then something along the same lines for the second part. Is this too cheap or incorrect somewhere? I'm kind of awful at rigor so any help would be greatly appreciated.