Definition:Little-Omega Notation/Informal Definition

Definition
Let $g: \N \to \R$ be a real sequence, expressed here as a real-valued function on the set of natural numbers $\N$.

$\omega$-notation is used to define a lower bound for $g$ which is not asymptotically tight.

Thus, let $f: \N \to \R$ be another real sequence, expressed here as a real-valued function on the set of natural numbers $\N$.

Then:
 * $\map f n = \map \omega {\map g n}$

means that $\map f n$ becomes arbitrarily large relative to $\map g n$ as $n$ approaches (positive) infinity.

Also see

 * Equivalence of Definitions of Little-Omega Notation