We can extend our notation to the case of two parameters n and m that can go to infinity independently at different rates. For a given function g(n, m), we denote by O(g(n, m)) the set of functions
O (g (n, m)) = {f(n, m): there exist positive constants c, n0, and m0
such that 0 ≤ f(n, m) ≤ cg(n, m)
for all n ≥ n0 and m ≥ m0}.
Give corresponding definitions for Ω(g(n, m)) and Θ(g(n, m)).
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