Category:Definitions/Little-Omega Notation

This category contains definitions related to little-$\omega$ notation.
Related results can be found in Category:Little-Omega Notation.

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

Then $\map \omega g$ is defined as:

$\map \omega g = \set {f: \N \to \R: \forall c \in \R_{>0}: \exists n_0 \in \N: \forall n > n_0: 0 \le c \cdot \size {\map g n} < \size {\map f n} }$