Definition:Little-O Notation/Real/Infinity

Definition
Let $f$ and $g$ be real-valued or complex-valued functions on a subset of $\R$ containing all sufficiently large real numbers.

Suppose $g(x)\neq0$ for $x$ sufficiently large.

The statement:
 * $f = o \left({g}\right)$

is equivalent to the statement:
 * $\displaystyle \lim_{x \to \infty} \ \frac{f \left({x}\right)} {g \left({x}\right)} = 0$

This statement is voiced $f$ is little-o of $g$ or simply $f$ is little-o $g$.