Definition:Little-O Notation/Real/Infinity/Definition 2

Definition
Let $f$ and $g$ be real functions defined on a neighborhood of $+ \infty$ in $\R$. $f$ is little-$\oo$ of $g$ as $x \to \infty$ :
 * $\forall \epsilon \in \R_{> 0}: \exists x_0 \in \R: \forall x \in \R: x \ge x_0 \implies \cmod {\map f x} \le \epsilon \cdot \cmod {\map g x}$

Also see

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