Symbols:Brackets/Square Brackets
Symbol
Square brackets are symbols used in a number of specific contexts.
They comprise the left (square) bracket $[$ and the right (square) bracket $]$.
The $\LaTeX$ code for \([\) is [ .
The $\LaTeX$ code for \(]\) is ] .
Usage
Square brackets are used in the following contexts:
- To contain the argument for the image of a subset under a mapping: $f \sqbrk T := \set {\map f x: x \in T}$
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The $\LaTeX$ code for \(\sqbrk {r_m r_{m - 1} \ldots r_2 r_1 r_0}_b\) is \sqbrk {r_m r_{m - 1} \ldots r_2 r_1 r_0}_b .
The $\LaTeX$ code for \(f \sqbrk T\) is f \sqbrk T .
Lowest Common Multiple: Deprecated Symbol
- $\sqbrk {a, b}$
The notation for the lowest common multiple is commonly seen as:
- $\sqbrk {a, b}$
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} .
Closed Interval
- $\closedint a b$
The closed interval between $a$ and $b$ is the set:
- $\closedint a b := a^\succcurlyeq \cap b^\preccurlyeq = \set {s \in S: \paren {a \preccurlyeq s} \land \paren {s \preccurlyeq b} }$
where:
- $a^\succcurlyeq$ 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 .
Closed Interval: Deprecated Symbol
- $\sqbrk {a, b}$
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} .
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 .
Right Half-Open Interval: Deprecated Symbol
- $\left [{a, b}\right)$
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) .
Half-Open Interval to the Left
- $\hointl a b$
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 .
Left Half-Open Interval: Deprecated Symbol
- $\left ({a, b}\right]$
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] .