Bounds

A set $A\subseteq \mathbb{R}$ is bounded above if there exists a number $b\in \mathbb{R}$ such that $a\le b$ for all $a\in A$. The number $b$ is called an upper bound for $A$.
Likewise, the set $A$ is bounded below if there exists a lower bound $l\in \mathbb{R}$ where $l\le a$ for every $a\in A$.