Symbols:Brackets/Square Brackets/Closed Interval

From ProofWiki
Jump to navigation Jump to search

Closed Interval

$\closedint a b$

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

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


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

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


$\sqbrk {a, b}$

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

$\sqbrk {a, b} := \set {x \in S: a \le x \le b}$

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

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