# Symbols:Brackets/Right Half-Open Interval

## Right Half-Open Interval

$\hointr a b$

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

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

where:

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

The $\LaTeX$ code for $\hointr a b$ is \hointr a b .

### Deprecated

$\left [{a, b}\right)$

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

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

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) .