Closed interval

A closed interval is an interval which has both a maximum and a minimum element. Closed intervals are denoted by $[a,b]$ where $a$ is the minimum and $b$ is the maximum. In the interval $[a,b]$ , $a$ is also the infimum (greatest lower bound) and $b$ is also the supremum (least upper bound). Alternatively, a closed interval $[a,b]$ is the set of all $x$ such that $x$ satisfies both of the inequalities $a \leq x$ and $x \leq b$ .