Problem 1 (25 marks) Let w E R \\ Q such that w > 0 i.e. @ is a positive irrational number. Define A = {m + nw ER| m + nw > 0 and m, ne Z} (a) Prove that if x, y E A and x > y, then x - y e A. (4 marks) (b) Prove that infA exists and infA 2 0