Problem 4. Define d : R2 - R. such that d((x1, X2), (y1, y2)) = max{|x1 - y1, x2 - y2/}. Show that d is a metric on R2. Problem 5. Let (S, d) be a metric space and (xi) be a sequence in S. Prove that if xi > x and xi + y, then x = y. Problem 6. Suppose x; + x and y; > y in (R, dE). Prove that xiyi > xy