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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 $c,n_0,$ and $m_0$ such that $0 \leq f(n,m) \leq cg(n,m)$ for all $n \geq n_0$ or $m \geq m_0$ }

Give corresponding definitions for $\Omega(g(n,m))$ and $\Theta(g(n,m))$.
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