Definition:Interval/Ordered Set/Half-Open

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

Let $a, b \in S$.

Hoare-Ramshaw Notation
The notation used on this site to denote an interval of an ordered set $\left({S, \preccurlyeq}\right)$ is a fairly recent innovation, and was introduced by C.A.R. Hoare and Lyle Ramshaw:

Also see

 * Definition:Ray (Order Theory)