Definition:Little-O Notation/Real/Infinity/Definition 1

Definition
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-$\mathcal o$ of $g$ as $x \to \infty$ :
 * $\ds \lim_{x \mathop \to \infty} \ \frac {\map f x} {\map g x} = 0$

Also see

 * Equivalence of Definitions of Little-O Notation for Real Functions