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.

Also see

• Definition:Strictly Monotone Real Function

• Results about monotone real functions can be found here.

Sources

• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 12.1$
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): monotonic function