Definition:Real Interval/Singleton

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Definition

Let $a, b \in \R$.

Consider the closed interval $\left [{a \,.\,.\, b} \right] \subseteq \R$.


When $a = b$:

$\left [{a \,.\,.\, b} \right] = \left [{a \,.\,.\, a} \right] = \left\{{x \in \R: a \le x \le a}\right\} = \left\{{a}\right\}$

Such an interval is sometimes referred to as a singleton interval.


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