\begin{definition}[Definition:Real Interval/Unbounded Open]
There are two '''unbounded open intervals''' involving a real number $a \in \R$, defined as:
{{begin-eqn}}
{{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}
}}
{{end-eqn}}
Using the same symbology, the set $\R$ can be represented as an '''unbounded open interval''' with no endpoints:
:$\openint \gets \to = \R$
\end{definition}