Big-Omega notation

Big-Omega notation is said to be the best case runtime of an algorithm. However formally it is simply a lower bound on the run time - the same as Big-O notation is simply an upper bound. This has a similar formal definition

$$ f = \Omega(g) \mbox{ if } \exists \ x_0 \in \mathbb{N}, m \in \mathbb{R}_{>0} \mbox{ such that } 0 \leq m \ast g(x) \leq f(x) \ \forall x > x_0.$$

This is just saying that $f$ eventually is at least a scalar multiple of $g$.