A sequence $$(a_n)_{n=0}^{\infty}$$ is increasing if $$a_n \le a_{n+1}$$ for all $$n \in \mathbb{N}$$ and decreasing if $$a_n \gt a_{n+1}$$ for all $$n \in \mathbb{N}$$. A sequence is monotone if it is either increasing or decreasing.