Definition:Big-Omega Notation

Definition
Big-Omega notation is a type of order notation for typically comparing 'run-times' or growth rates between two growth functions.

Suppose $$f, g$$ are two functions.

Then $$f(n) \in \Omega (g(n))$$ iff $$\exists c > 0, k \ge 0: \forall n > k: f(n) \ge c g(n)$$.

This is read as "f(n) is big omega of g(n)".

Another method of determining the condition is the following limit:


 * $$\lim_{ n \to \infty} {\frac{f(n)}{g(n)}} = c > 0$$, where $$0 < c \le \infty$$.

If such a c does exist, then $$f(n) \in \Omega (g(n))$$.