1. The problem statement, all variables and given/known data Show that the set S ⊆ C[0, 1] consisting of continuous functions which map Q to Q is dense, where the metric on C[0, 1] is defined by d(f,g) = max |f(x)−g(x)|. All else I need to know is what the question doesn't mention - what the set is dense in? I assume it doesn't mean dense in itself since it probably wouldn't bother giving a specific space then, so do you think it means the set of continuous R->R functions on [0,1] or all R->R functions on [0,1], or what? Just need to actually understand what it means before I can get going - thanks!