# Symbols:Brackets/Left Half-Open Interval

## Left Half-Open Interval

$\hointl a b$

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

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

where:

$a^\succ$ 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 .

### Deprecated

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

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] .