# Definition:Monotone (Order Theory)/Real Function

## Definition

This definition continues to hold when $S = T = \R$.

Thus, let $f$ be a real function.

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

## Also known as

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

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