Definition:O Notation/Little-O Notation/Sequence/Definition 1

Definition
Let $\sequence {a_n}$ and $\sequence {b_n}$ be sequences of real or complex numbers. Let $b_n\neq0$ for all $n$.

$a_n$ is little-O of $b_n$
 * $\ds \lim_{n \mathop \to \infty} \frac {a_n} {b_n} = 0$