(a) Prove that f ∈ O(f) for all f: Z+ R.
(b) Let f, g: Z+ → R. If f ∈ O (g) and g ∈ 0(f), prove that 0(f) = 0(g). That is, prove that for all h: Z+ R, if h is dominated by f, then h is dominated by g, and conversely.
(c) If f, g: Z+ → R, prove that if 0(f) = 0(g), then f ∈ 0(g) and g ∈ O(f).