Symbols:Brackets/Round Brackets
Symbol
Round brackets are the symbols most used for placing an expression in parenthesis.
They comprise the left (round) bracket $($ and the right (round) bracket $)$.
The $\LaTeX$ code for \((\) is ( .
The $\LaTeX$ code for \()\) is ) .
Usage
Round brackets are used in the following contexts:
- To denote binding priority, for example $a \times \paren {b + c}$
- To denote an ordered tuple: $\tuple {a_1, a_2, a_2, a_4}$
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The $\LaTeX$ code for \(a \times \paren {b + c}\) is a \times \paren {b + c} .
The $\LaTeX$ code for \(\tuple {a_1, a_2, a_2, a_4}\) is \tuple {a_1, a_2, a_2, a_4} .
The $\LaTeX$ code for \(\map f {x, y}\) is \map f {x, y} .
Binomial Coefficient
- $\dbinom n m$
The binomial coefficient, which specifies the number of ways you can choose $m$ objects from $n$ (all objects being distinct).
Formally defined as:
- $\dbinom n m = \begin {cases}
\dfrac {n!} {m! \, \paren {n - m}!} & : m \le n \\ 0 & : m > n \end {cases}$
The $\LaTeX$ code for \(\dbinom {n} {m}\) is \dbinom {n} {m} or \ds {n} \choose {m}.
Greatest Common Divisor: Deprecated Symbol
- $\tuple {a, b}$
The notation for the greatest common divisor is commonly seen as:
- $\tuple {a, b}$
However, as the $\tuple {a, b}$ notation is ambiguous, its use is deprecated on $\mathsf{Pr} \infty \mathsf{fWiki}$.
The $\LaTeX$ code for \(\tuple {a, b}\) is \tuple {a, b} .
Open Interval
- $\openint a b$
The open interval between $a$ and $b$ is the set:
- $\openint a b := a^\succ \cap b^\prec = \set {s \in S: \paren {a \prec s} \land \paren {s \prec b} }$
where:
- $a^\succ$ denotes the strict upper closure of $a$
- $b^\prec$ denotes the strict lower closure of $b$.
The $\LaTeX$ code for \(\openint a b\) is \openint a b .
Open Interval: Deprecated Symbol
- $\tuple {a, b}$
The notation for a Open interval is more commonly seen as:
- $\tuple {a, b} := \set {x \in S: a < x < b}$
However, as the $\tuple {a, b}$ notation is ambiguous, its use is deprecated on $\mathsf{Pr} \infty \mathsf{fWiki}$.
The $\LaTeX$ code for \(\tuple {a, b}\) is \tuple {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] .