\begin{definition}[Definition:Interval/Notation/Wirth]
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 {{AuthorRef|Niklaus Emil Wirth}}:
{{begin-eqn}}
{{eqn | l = \openint a b
      | o = :=
      | r = \set {s \in S: \paren {a \prec s} \land \paren {s \prec b} }
      | c = Open Interval
}}
{{eqn | l = \hointr a b
      | o = :=
      | r = \set {s \in S: \paren {a \preccurlyeq s} \land \paren {s \prec b} }
      | c = Right Half-Open Interval
}}
{{eqn | l = \hointl a b
      | o = :=
      | r = \set {s \in S: \paren {a \prec s} \land \paren {s \preccurlyeq b} }
      | c = Left Half-Open Interval
}}
{{eqn | l = \closedint a b
      | o = :=
      | r = \set {s \in S: \paren {a \preccurlyeq s} \land \paren {s \preccurlyeq b} }
      | c = Closed Interval
}}
{{end-eqn}}
The term '''Wirth interval notation''' has consequently been coined by {{ProofWiki}}.
\end{definition}