Definition:Real Interval/Closed

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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.


Example $1$

Let $I$ be the closed real interval defined as:

$I := \closedint 1 3$

Then $3 \in I$.

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.