# 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: $\tuple {a_1, a_2, a_2, a_4}$

This article is complete as far as it goes, but it could do with expansion.In particular: Plenty more usages, if only I could think of themYou can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Expand}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

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]`

.