\begin{definition}[Definition:Big-Omega]
'''Big-Omega notation''' is a type of order notation for typically comparing 'run-times' or growth rates between two growth functions.
Let $f, g$ be two functions.
{{explain|Domain and range of $f$ and $g$ to be specified: reals?}}
Then:
:$\map f n \in \map \Omega {\map g n}$
{{iff}}:
:$\exists c > 0, k \ge 0: \forall n > k: \map f n \ge c \map g n$
This is read as:
:'''$\map f n$ is big omega of $\map g n$'''.
{{ExtractTheorem|Put the below into separate pages, either as a 2nd definition or just an equivalence proof}}
Another method of determining the condition is the following limit:
:$\ds \lim_{n \mathop \to \infty} {\frac {\map f n} {\map g n} } = c > 0$
where $0 < c \le \infty$.
If such a $c$ does exist, then:
:$\map f n \in \map \Omega {\map g n}$
{{ExtractTheorem|The below into its own page}}
To say that $\map f n \in \map \Omega {\map g n}$ is equivalent to:
:$\map g n \in \map \OO {\map f n}$
where $\OO$ is the big-O notation.
\end{definition}