Definition:Interval/Ordered Set/Right Half-Open

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

Let $a, b \in S$.

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

It is written $\left[{a \,.\,.\, b}\right)$.

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