Suppose that f: R → R is a function such that f(x+y) = f(x) + f(y) for every x, y E R. Prove that f has a limit at 0 if and only if f has a limit at every c ER. Hints: The "if" part is trivial, so it's the "only if" part that requires work. Hints to do this: first show that f(1/n) = f(1)/n for any natural number n. Now show that if f has a limit at 0, then the limit itself must be 0. Complete the proof from there.

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