1. The problem statement, all variables and given/known data Let (X,d) be a metric space, M a positive number, and f: X->X a continuous function for which: d(f(x), f(y)) is less than or equal to Md(x,y) for all x, y in X. Prove that f is continuous. Use this to conclude that every contractive function is continuous. 3. The attempt at a solution It seems intuitively obvious that f is continuous, but there are a couple of things throwing me off on this one. First, it's asking about concluding that contractive functions are continuous, but this isn't by definition a contractive function that we're looking at since M >1 is a possibility. And second, the problem 'gives' that f is continuous and then asks you to prove that f is continuous. Help!