Definition:Strictly Increasing/Real Function

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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.

Also see