Definition:Interval/Ordered Set/Endpoint

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

Let $a, b \in S$.

Let:
 * $\left[{a \,.\,.\, b}\right]$

or
 * $\left[{a \,.\,.\, b}\right)$

or
 * $\left({a \,.\,.\, b}\right]$

or
 * $\left({a \,.\,.\, b}\right)$

be an interval.

The elements $a, b \in S$ are known as the endpoints (or end points) of the interval.

$a$ is sometimes called the left hand endpoint and $b$ the right hand end point of the interval.

Also known as
The endpoints can also be written as end points.