# Definition:Strictly Increasing/Real Function

## Definition

Let $f$ be a real function.

Then $f$ is strictly increasing if and only if:

$x < y \implies f \left({x}\right) < f \left({y}\right)$

## Also known as

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

Some sources give it as a strictly monotonic increasing function