Definition:Little-O Notation/Sequence/Definition 1

Definition
Let $\left \langle {a_n} \right \rangle$ and $\left \langle {b_n} \right \rangle$ be sequences of real or complex numbers.

$a_n$ is little-O of $b_n$
 * $\forall \epsilon \in \R: \epsilon > 0 : \exists n_0 \in \N : \left({n \ge n_0 \implies \left\vert{a_n}\right\vert \le \epsilon \cdot \left\vert{b_n}\right\vert}\right)$

That is:
 * For all $\epsilon>0$, $\left\vert{a_n}\right\vert \le \epsilon \cdot \left\vert{b_n}\right\vert$

for all sufficiently large $n$.