Definition:Theta Notation/Definition 2

Definition
Let $f: \N \to \R, g: \N \to \R$ be two real sequences, expressed here as real-valued functions on the set of natural numbers $\N$.

Let there exist $c \in \R_{>0}$ such that:
 * $\ds \lim_{n \mathop \to \infty} \frac {\map f n} {\map g n} = c$

Then:
 * $\map f n \in \map \Theta {\map g n}$

Also see

 * Equivalence of Definitions of Theta Notation