Monotone sequence

A sequence $\{x_n\}$ such that for all $n=1,2,\dots,$ either

$x_n<x_{n+1}$ (a strictly-increasing sequence);

$x_n\leq x_{n+1}$ (a non-decreasing sequence);

$x_n>x_{n+1}$ (a strictly-decreasing sequence); or

$x_n\geq x_{n+1}$ (a non-increasing sequence).

Comments

See also Increasing sequence; Decreasing sequence.