Definition:O Notation/Little-O Notation/Real Functions/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 $g(x)\neq0$ for $x$ sufficiently large.

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

$\displaystyle \lim_{x \to \infty} \ \frac{f \left({x}\right)} {g \left({x}\right)} = 0$