Definition:Increasing/Real Function

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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 an increasing (real) function 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.

Also see

  • Results about increasing real functions can be found here.