1. The problem statement, all variables and given/known data Prove: If f is defined on the reals and continuous at x=0, and if f(x1+x2)=f(x1)+f(x2) for all x1,x2 in the reals, then f is continuous at all x in the reals. 2. Relevant equations Using defn of limits and continuity 3. The attempt at a solution is this like proving that the sum of two functions is continuous? I am a bit confused, this is the last on of the homework, then I can enjoy my easter.