# Increasing function

## Definition

An **increasing function** (sometimes called a **strictly increasing function**) is a function satisfying the following condition for any two distinct elements in its domain:

*Note*: Sometimes the term *increasing* is used for a non-decreasing function, where we do not require *strict* inequality but only insist on .

Also note that for functions whose domain is empty or a single point, the definition of being increasing is vacuously satisfied and is uninteresting.