\begin{definition}[Definition:Real Interval Types]
It is usual to define intervals in terms of inequalities.
These are in the form of a pair of brackets, either round or square, enclosing the two endpoints of the interval separated by two dots.
Whether the bracket at either end is round or square depends on whether the end point is '''inside''' or '''outside''' the interval, as specified in the following.
Let $a, b \in \R$ be real numbers.
\end{definition}