Monotonicity

Definition: A function $y(x)$ is increasing on an interval if for all $x$ in the interval and $\Delta x>0$

$$y(x+\Delta x)\geq y(x).$$

A function $y(x)$ is decreasing on an interval if for all $x$ in the interval and $\Delta x>0$
$$y(x+\Delta x)\leq y(x).$$

A function is monotonic on an interval if the function is either increasing or decreasing on the interval.

Remark: Monotonicity is defined non-strictly. This implies that $\geq$ and $\leq$ are used in the requirements instead of $>$ and $<$, respectively.