\begin{definition}[Definition:Little-Omega]
Let $f$ and $g$ be real functions.
Then:
:$\map f n \in \map \omega {\map g n}$
is equivalent to:
:$\ds \lim_{n \mathop \to \infty} {\frac {\map f n} {\map g n} } = \infty$
{{ExtractTheorem|Extract this into a separate page with proof}}
A function $f$ is $\map \omega g$ {{iff}} $f$ is not $\map \OO g$ where $\OO$ is the big-O notation.
\end{definition}