Function f is Big-O of g iff g is Big-Omega of f

Theorem
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 $\N$.

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


 * $\map g n \in \map \Omega {\map f n}$
 * $\map g n \in \map \Omega {\map f n}$

where:
 * $\OO$ denotes big-$\OO$ notation
 * $\Omega$ denotes big-$\Omega$ notation.