Limit Lemma

The asymptotic relationship between two positive functions can be determined by dividing their horizontal asymptotes.

$$\underset{n\to \infty }{\lim }\frac{f(n)}{g(n)}=L$$

Condition	Asymptotic Relationship
$L=0$	$f(n)=O(g(n))$
$L=\infty$	$f(n)=\Omega (g(n))$
$L=c>0$	$f(n)=\Theta (g(n))$