\begin{definition}[Definition:Real Interval/Notation/Wirth]
The notation used on this site to denote a real interval is a fairly recent innovation, and was introduced by {{AuthorRef|Niklaus Emil Wirth}}:
{{begin-eqn}}
{{eqn | l = \openint a b
      | o = :=
      | r = \set {x \in \R: a < x < b}
      | c = Open Real Interval
}}
{{eqn | l = \hointr a b
      | o = :=
      | r = \set {x \in \R: a \le x < b}
      | c = Half-Open (to the right) Real Interval
}}
{{eqn | l = \hointl a b
      | o = :=
      | r = \set {x \in \R: a < x \le b}
      | c = Half-Open (to the left) Real Interval
}}
{{eqn | l = \closedint a b
      | o = :=
      | r = \set {x \in \R: a \le x \le b}
      | c = Closed Real Interval
}}
{{end-eqn}}
The term '''Wirth interval notation''' has consequently been coined by {{ProofWiki}}.
\end{definition}