The following is analogous to the "big-Oh" notation introduced in conjunction with Definition 5.23.
For f, g: Z+ → R we say that / is of order at least g if there exist constants M ∈ R+ and f: ∈ Z+ such that |f(n)| > M\g(n) for all n ∈ Z+, where n > k. In this case we write f ∈ Ω (g) and say that f is "big Omega of g." So Ω (g) represents the set of all functions with domain Z+ and codomain R that dominate g.
Suppose that f, g, h: Z+ → R, where f(n) = 5n2 + 3n, g(n) = n2, h(n) = n, for all n ∈ Z+. Prove that (a) f ∈ Ω (g); (b) g ∈ Ω (f); (c) f ∈ Ω(h); and (d) h ∈ Q(f) - that is, h is not "big Omega of f."