# Symbols:O/Big-O Notation

## Big-O Notation

$\OO$

Used for example as follows in the context of sequences:

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

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

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

The $\LaTeX$ code for $a_n = \map \OO {b_n}$ is a_n = \map \OO {b_n} .