Symbols:Brackets/Round Brackets/Open Interval

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Open Interval

$\openint a b$

The open interval between $a$ and $b$ is the set:

$\openint a b := a^\succ \cap b^\prec = \set {s \in S: \paren {a \prec s} \land \paren {s \prec b} }$


$a^\succ$ denotes the strict upper closure of $a$
$b^\prec$ denotes the strict lower closure of $b$.

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


$\tuple {a, b}$

The notation for a Open interval is more commonly seen as:

$\tuple {a, b} := \set {x \in S: a < x < b}$

However, as the $\tuple {a, b}$ notation is ambiguous, its use is deprecated on $\mathsf{Pr} \infty \mathsf{fWiki}$.

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