1. The problem statement, all variables and given/known data Let f be a continuous function lR (all real numbers) --> lR such that f(x+y) = f(x) + f (y) for x, y in lR. prove that f(n) = n*f(1) for all n in lN (all natural numbers) 2. Relevant equations f is continuous also note and prove that f(0) = 0 3. The attempt at a solution Edit: I figured out the general proof using induction, assuming that the base case f(0) is true: Assuming f(n) = nf(1), prove that f(n+1) = (n+1)f(1): we know f(x+y) =f(x) + f (y) so f(n+1) =f(n) + f (1) and according to inductive hypothesis, f(n) = nf(1) s0 f(n) + f (1) = nf(1) + f (1) =(n+1)f(1). But I still don't understand why the base case f(0) = 0 is true..?