1. The problem statement, all variables and given/known data If f: ℝ → ℝ is a continuous function with the property that its range is contained in the set of integers, prove that f must be a constant function. 2. Relevant equations 3. The attempt at a solution I know why this is true, I just don't know how to begin an actual proof. So far I've thought of proving by contradiction, with letting f be discontinuous and use f(x) = [x], whose range set is contained in Z. I seem to have trouble with the format of a formal proof.