\begin{definition}[Definition:Interval/Ordered Set/Endpoint]
Let $\struct {S, \preccurlyeq}$ be an ordered set.
Let $a, b \in S$.
Let:
:$\closedint a b$
or
:$\hointr a b$
or
:$\hointl a b$
or
:$\openint a b$
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.
\end{definition}