Big O Notation

Definitions

Big O: There exists $c>0$ and $n_0$ such that $0\le f(n)\le cg(n)$ such that $n\ge n_0$
Big Omega: There exists $c>0$ and $n_0$ such that $cg(n)\le f(n)$ such that $n\ge n_0$
Big Theta: The asymptotic function that is both big O and big omega.