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 $x \to \infty$ if and only if:

$\forall \epsilon \in \R_{> 0}: \exists x_0 \in \R: \forall x \in \R: x \ge x_0 \implies \cmod {\map f x} \le \epsilon \cdot \cmod {\map g x}$

Also see

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