Definition:Little-O Notation/Sequence/Definition 1

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

$a_n$ is little-O of $b_n$
 * $\forall \epsilon \in \R_{>0}: \exists n_0 \in \N: \forall n \in \N: \paren {n \ge n_0 \implies \cmod {a_n} \le \epsilon \cdot \cmod {b_n} }$

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

for all sufficiently large $n$.