Definition:Strictly Increasing/Real Function

Definition
Let $f$ be a real function.

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

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

Some sources give it as a strictly monotonic increasing function

Also see

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