# Definition:Little-Omega

## Definition

Let $f$ and $g$ be real functions.

Then:

$\map f n \in \map \omega {\map g n}$

is equivalent to:

$\ds \lim_{n \mathop \to \infty} {\frac {\map f n} {\map g n} } = \infty$

A function $f$ is $\map \omega g$ if and only if $f$ is not $\map \OO g$ where $\OO$ is the big-O notation.