Definition:Increasing/Real Function

Definition
Let $f$ be a real function.

Then $f$ is increasing :
 * $x \le y \implies \map f x \le \map f y$

Also known as
Some sources refer to this as a non-decreasing real function, and use the term increasing real function for what on is called a strictly increasing real function.

Some sources give this as monotonic increasing function.

Also see

 * Definition:Strictly Increasing Real Function
 * Definition:Decreasing Real Function
 * Definition:Monotone Real Function