Definition:Real Interval/Closed

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Definition

Let $a, b \in \R$.

The closed (real) interval from $a$ to $b$ is defined as:

$\closedint a b = \set {x \in \R: a \le x \le b}$


Also known as

Such an interval can also be referred to as compact.


Some sources do not explicitly define an open interval, and merely to a closed real interval as an interval. Such imprecise practice is usually discouraged.


Also see


Technical Note

The $\LaTeX$ code for \(\closedint {a} {b}\) is \closedint {a} {b} .

This is a custom $\mathsf{Pr} \infty \mathsf{fWiki}$ command designed to implement Wirth interval notation.


Sources