Definition:Real Interval/Empty

Definition
Let $a, b \in \R$.

Let $\left [{a \,.\,.\, b} \right]$, $\left [{a \,.\,.\, b} \right)$, $\left ({a \,.\,.\, b} \right)$ and $\left ({a \,.\,.\, b} \right)$ be real intervals: closed, half-open and open as defined.

When $a > b$:

When $a = b$:

Such empty sets are referred to as empty intervals.