Let (V, ) be a normed vector space. (a) Prove that, for all x, y V, |||*||- ||y|||||x-y||. (b) Let {x()}KEN be a convergent sequence in V with limit V. Prove that (Hint: Use part (a).) (c) Let {x()}KEN be a sequence in V and x, y V. Prove that, if x(k) x, and x(k) y, then = lim ||k) || = ||||. k = y.