Definition:Monotone (Order Theory)/Real Function

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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

  • Results about monotone real functions can be found here.