(a) { r₁ + ir₂ ; r₁,r₂ Î Q } is a countable dense subset of C. Hence C is a separable Banach algebra.

(b) l^¥ isn't separable. In fact if S = {a₁, a₂, ¼, } is a countable set in l^¥, a_n = (a_n^k)_{k Î N}, and