# 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 $x \leq b$.

Every closed interval is a closed set.

## Examples

$[-1,1]$, the set of real numbers nonstrictly between $-1$ and $1$, is a closed interval.

For any real number $x$, the set $\{x\} = [x,x]$ containing only $x$ is a closed interval.