Definition:Theta Notation/Informal Definition

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


 * $f$ is $\Theta$ of $g$


 * there exist positive constants $c_1$ and $c_2$ such that $\map f n$ can be "sandwiched" between $c_1 \map g n$ and $c_2 \map g n$ for sufficiently large $n \ge n_0$.
 * there exist positive constants $c_1$ and $c_2$ such that $\map f n$ can be "sandwiched" between $c_1 \map g n$ and $c_2 \map g n$ for sufficiently large $n \ge n_0$.

It is not as important to determine the values of $c_1$, $c_2$ as it is to establish that such constants exist.