Definition:Interval/Ordered Set/Left Half-Open

Definition
Let $\left({S, \preceq}\right)$ be an ordered set.

Let $a, b \in S$.

Then $\left\{{s \in S: \left({a \prec s}\right) \land \left({s \preceq b}\right)}\right\}$ is called the left half-open interval between $a$ and $b$.

It is written $\left({a \,.\,.\, b}\right]$.

Also defined as
Some sources require that $a \preceq b$.