Definition:Real Interval/Open

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Definition

Let $a, b \in \R$.

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

$\openint a b := \set {x \in \R: a < x < b}$


Examples

Example $1$

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

$I := \openint 1 2$

Then $3 \notin I$.


Example $2$

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

$I := \openint 0 2$

Then $2 \notin I$.


Also see


Technical Note

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

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


Sources