Real function/Strictly increasing/Definition

Strictly increasing function

Let ${}I\subseteq \mathbb {R}$ denote an interval and let

$f\colon I\longrightarrow \mathbb {R}$

denote a function. Then ${}f$ is called strictly increasing if

$f(x')>f(x){\text{ holds for all }}x,x'\in I{\text{ with }}x'>x.$