Let f : R †’ R be such that f(x + y) = f(x) + f(y) for all x, y in R. Assume that exists. Prove that L = 0, and then prove that f has a limit at every point c ˆˆ R. [First note that F(2x) = f(x) + f(x) = 2f(x) for x ˆˆ R. Also note that f(x) = f(x - c) + f(c) for x, c in R.]

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lim f = L