2. (a) Let B be a non-empty subset of real numbers that is bounded below with lower bound B E R. Prove that B = inf(B) if and only if there exists a sequence (bn) such that bn E B for each n E N and lim(bn) = B. (b) Let A be a non-empty subset of real numbers that is bounded above with a > -1 for all a E A. Define B to be the set B = 1 - : a E A Using part (a), or otherwise, prove that inf(B) exists and 1 inf (B) = 1+ sup( A) (c) Prove that sup(A) = 2/3 with 4n - 3 A = -:nENS. 6n (d) Using part (b), or otherwise, prove that the infimum of 6n B = 10n - 3 inEN exists and find its value explicitly. [19 markel