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

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Definition

Let $f$ and $g$ be real functions defined on a neighborhood of $+ \infty$ in $\R$.

Let $\map g x \ne 0$ for $x$ sufficiently large.


$f$ is little-$\oo$ of $g$ as $x \to \infty$ if and only if:

$\ds \lim_{x \mathop \to \infty} \frac {\map f x} {\map g x} = 0$


Also see


Sources