**Definition (Increasing)** Let $E \subset \mathbb{R}$. A given function $f: E \to \mathbb{R}$ is *increasing* if $x \geq y \implies f(x) \geq f(y)$ and *strictly increasing* if $x >y \implies f(x)>f(y)$. **Definition (Decreasing)**: A given [[Function|function]] $f:E \to \mathbb{R}$ is '*decreasing*' if for all $x\leq y$, $f(x) \geq f(y)$ . A function is (strictly) *monotonic* if it's (strictly) increasing or (strictly) decreasing. See **Applications** [[Integral test for convergence of series of non-negative decreasing function]]; [[Inverse of Strictly Monotonic Continuous Real Function Exists, is Strictly Monotonic in the Same Sense, and is Continuous]].