# Definition:Increasing/Real Function

## Definition

Let $f$ be a real function.

Then $f$ is increasing if and only if:

$x \le y \implies \map f x \le \map f y$

## Also known as

Some sources refer to this as a non-decreasing real function, and use the term increasing real function for what on $\mathsf{Pr} \infty \mathsf{fWiki}$ is called a strictly increasing real function.

Some sources give this as monotonic increasing function.