A function $f(n)$ is **monotonically increasing** if $m \le n$ implies $f(m) \le f(n)$. In other words, the function does not decrease as $n$ increases. A function is **strictly increasing** if $f(m) < f(n)$. A function $f(n)$ is **monotonically decreasing** if $m \le n$ implies $f(m) \ge f(n)$ or the function does not increase as $n$ increases. A function is **strictly decreasing** if $f(m) > f(n)$.