# Definition:Little-Omega

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## Definition

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

Then:

- $f \left({n}\right) \in \omega \left({g \left({n}\right)}\right)$

is equivalent to:

- $\displaystyle \lim_{n \to \infty} {\frac{f \left({n}\right)} {g \left({n}\right)}} = \infty$

A function $f$ is $\omega \left({g}\right)$ iff $f$ is not $\mathcal O \left({g}\right)$ where $\mathcal O$ is the big-O notation.