Analysis I. Sheet 2. Question 3(iii). I think that sup(f(S)) = f(sup(S)) should be sup(f(S)) <= f(sup(S)). For example, define the increasing function f: R --> R by: f(x) = x, for all x < 1. f(x) = x + 1, for all x >= 1. Take S to be the open interval (0,1). Then f(S) = (0,1), so sup(f(S)) sup((0,1)) = 1. But sup(S) = 1, so f(sup(S)) = f(1) = 2. Analysis I. Sheet 4. Question 3(iii). The second occurrence of u_n should be w_n. Analysis I : Sheet 7 Question 3 I apologise for two typos : (i) In part (a) both sums should start at 0. (ii) In part (c) the exponent of (1-x) is -(k+1) and not -k.