\begin{definition}[Definition:Real Interval/Definition 2]
A '''real interval''' is a subset of $\R$ that is one of the following real interval types:
* closed bounded interval
* open bounded interval
* left half-open bounded interval
* right half-open bounded interval
* closed and bounded on the right, also known as a closed unbounded below real interval
* open and bounded on the right, also known as an open unbounded below real interval
* closed and bounded on the left, also known as a closed unbounded above real interval
* open and bounded on the left, also known as an open unbounded above real interval
* unbounded interval without endpoints
\end{definition}