\begin{definition}[Definition:O Notation/Little-O Notation/Real Functions/Definition 1]
Let $f$ and $g$ be real-valued or complex-valued functions on a subset of $\R$ containing all sufficiently large real numbers.
Let $\map g x \ne 0$ for $x$ sufficiently large.
'''$f$ is little-o of $g$''' as $x \to \infty$ {{Iff}}:
:$\ds \lim_{x \mathop \to \infty} \ \frac {\map f x} {\map g x} = 0$
\end{definition}