Definition:Little-Omega Notation

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 $\map \omega g$ $f$ is not $\map \OO g$ where $\OO$ is the big-$\OO$ notation.

Also see

 * Definition:O Notation


 * Definition:Big-Omega Notation