Definition:Big-O Notation/Sequence/Definition 1

Definition
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:


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

Also see

 * Equivalence of Definitions of Big-O Notation for Sequences