Hi, here is the question, if A is a closed set that contains every rational number r: [0,1], show that [0,1] is a subset of A. But, how could A be closed? If A is closed, R^n-A is open, so any point in R^n-A would have a open sphere around it and this open sphere wouldn't intersect A. apparently, this is not true. eg. sqrt(0.5) has no open sphere around it that is disjoint from A.