Monotonic Sequences

A Sequence $(a_n)$ is

• increasing if $\mathrm{\forall }n\in \mathbb{N}$ we have $a_n\le a_{n+1}$
• decreasing if $\mathrm{\forall }n\in \mathbb{N}$ we have $a_n\ge a_{n+1}$
• monotone if it is either increasing or decreasing.