Definition:Interval/Ordered Set

Definition
Let $\struct {S, \preccurlyeq}$ be an ordered set.

Let $a, b \in S$.

The intervals between $a$ and $b$ are defined as follows:

Wirth Interval Notation
The notation used on this site to denote an interval of an ordered set $\struct {S, \preccurlyeq}$ is a fairly recent innovation, and was introduced by :

Also see

 * Definition:Ray (Order Theory)