# Definition:Strictly Monotone/Real Function

## Definition

Let $f: S \to \R$ be a real function, where $S \subseteq \R$.

Then $f$ is strictly monotone if and only if it is either strictly increasing or strictly decreasing.

## Also known as

A strictly monotone function can also be referred to as a strictly monotonic function.

Strictly monotone is preferred on $\mathsf{Pr} \infty \mathsf{fWiki}$ because it is shorter and has less syllables, and hence is more economical.