Half-open interval

A half-open interval is an interval which has either a maximum or a minimum element but not both.

If a half-open interval has a minimum $a$ but no maximum, then it is denoted by $[a,b)$ , where $b$ is the supremum (least upper bound), or $\infty$ if no supremum exists. Alternatively, $[a,b)$ is the set of all $x$ such that $a \leq x$ and $x < b$ .

If a half-open interval has a maximum $b$ but no minimum, then it is denoted by $(a,b]$ , where $a$ is the infimum (greatest lower bound), or $-\infty$ if no infimum exists. Alternatively, $(a,b]$ is the set of all $x$ such that $a < x$ and $x \leq b$ .