# Definition:Monotone (Order Theory)/Real Function

< Definition:Monotone (Order Theory)(Redirected from Definition:Monotone Real Function)

## Contents

## 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.

## Also see

## Sources

- 1977: K.G. Binmore:
*Mathematical Analysis: A Straightforward Approach*... (previous) ... (next): $\S 12.1$