\begin{definition}[Definition:Real Interval/Notation/Reverse-Bracket]
In order to avoid the ambiguity problem arising from the conventional notation for intervals where an open real interval can be confused with an ordered pair, some authors use the '''reverse-bracket notation''' for open and half-open intervals:
{{begin-eqn}}
{{eqn | l = \left ] {\, a, b} \right [
      | o = :=
      | r = \set {x \in \R: a < x < b}
      | c = Open real interval
}}
{{eqn | l = \left [ {a, b} \right [
      | o = :=
      | r = \set {x \in \R: a \le x < b}
      | c = Half-open on the right
}}
{{eqn | l = \left ] {\, a, b} \right ]
      | o = :=
      | r = \set {x \in \R: a < x \le b}
      | c = Half-open on the left
}}
{{end-eqn}}
These are often considered to be both ugly ''and'' confusing, and hence are limited in popularity.
Category:Definitions/Real Intervals
\end{definition}