Symbols:Brackets/Left Half-Open Interval

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Left Half-Open Interval

$\hointl a b$

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

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


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

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


$\left ({a, b}\right]$

The notation for a left half-open interval is more commonly seen as:

$\left ({a, b}\right] := \set {x \in S: a < x \le b}$

However, for consistency with other interval notation, its use is deprecated on $\mathsf{Pr} \infty \mathsf{fWiki}$.

The $\LaTeX$ code for \(\left ({a, b}\right]\) is \left ({a, b}\right] .