\begin{definition}[Definition:Real Interval/Notation/Conventional]
These are the notations usually seen for real 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 real interval
}}
{{eqn | l = \left ({a, b}\right]
      | o = :=
      | r = \set {x \in \R: a < x \le b}
      | c = Half-open real interval
}}
{{eqn | l = \left [{a, b}\right]
      | o = :=
      | r = \set {x \in \R: a \le x \le b}
      | c = Closed real interval
}}
{{end-eqn}}
but they can be confused with other usages for this notation.
In particular, there exists the danger of taking $\paren {a, b}$ to mean an ordered pair.
Category:Definitions/Real Intervals
\end{definition}