\begin{definition}[Definition:Interval/Notation/Unbounded Intervals]
In Wirth interval notation, unbounded intervals of an ordered set $\struct {S, \preccurlyeq}$ are written as follows:
{{begin-eqn}}
{{eqn | l = \hointr a \to
      | o = :=
      | r = \set {x \in S: a \preccurlyeq x}
}}
{{eqn | l = \hointl \gets a
      | o = :=
      | r = \set {x \in S: x \preccurlyeq a}
}}
{{eqn | l = \openint a \to
      | o = :=
      | r = \set {x \in S: a \prec x}
}}
{{eqn | l = \openint \gets a
      | o = :=
      | r = \set {x \in S: x \prec a}
}}
{{eqn | l = \openint \gets \to
      | o = :=
      | r = \set {x \in S} = S
}}
{{end-eqn}}
Category:Definitions/Intervals
\end{definition}