\begin{definition}[Definition:Real Interval/Notation/Unbounded Intervals]
Some authors (sensibly, perhaps) prefer not to use the $\infty$ symbol and instead use $\to$ and $\gets$ for $+\infty$ and $-\infty$ repectively.
In Wirth interval notation, such intervals are written as follows:
{{begin-eqn}}
{{eqn | l = \hointr a \to
      | o = :=
      | r = \set {x \in \R: a \le x}
}}
{{eqn | l = \hointl \gets a
      | o = :=
      | r = \set {x \in \R: x \le a}
}}
{{eqn | l = \openint a \to
      | o = :=
      | r = \set {x \in \R: a < x}
}}
{{eqn | l = \openint \gets a
      | o = :=
      | r = \set {x \in \R: x < a}
}}
{{eqn | l = \openint \gets \to
      | o = :=
      | r = \set {x \in \R} = \R
}}
{{end-eqn}}
In reverse-bracket notation, they appear as:
{{begin-eqn}}
{{eqn | l = \left [{a, \to} \right]
      | r = \set {x \in \R: a \le x}
      | c = 
}}
{{eqn | l = \left [{\gets, a} \right]
      | r = \set {x \in \R: x \le a}
      | c = 
}}
{{eqn | l = \left ]{\, a, \to} \right]
      | r = \set {x \in \R: a < x}
      | c = 
}}
{{eqn | l = \left [{\gets, a \,} \right[
      | r = \set {x \in \R: x < a}
      | c = 
}}
{{end-eqn}}
Category:Definitions/Real Intervals
\end{definition}