Definition:Strictly Monotone/Real Function

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

Then $f$ is strictly monotone 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 because it is shorter and has less syllables, and hence is more economical.

Also see

 * Definition:Increasing Real Function
 * Definition:Decreasing Real Function
 * Definition:Monotone Real Function