# Symbols:Brackets/Braces

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## Symbol

Braces is the name given to the pair of curly brackets:

$\set {\cdots}$

The $\LaTeX$ code for $\{$ is \{  or \lbrace.

The $\LaTeX$ code for $\}$ is \}  or \rbrace.

## Usage

Braces are conventionally used in the following contexts:

Set delimiters, to membership of sets and classes, for example: $\set {a, b, c}$
Karamata notation for the Stirling numbers of the second kind:
$\ds {n \brace k}$
To denote a Laplace transform: $\laptrans {\map f t}$
In a definition by cases, for example: $n! = \begin{cases} 1 & : n = 0 \\ n \paren {n - 1} & : n \ne 0 \end{cases}$

On $\mathsf{Pr} \infty \mathsf{fWiki}$, which implements the $\LaTeX$ mathematical markup language, braces are also used to delimit arguments to $\LaTeX$ commands.

The $\LaTeX$ code for $\set {a, b, c}$ is \set {a, b, c} .

The $\LaTeX$ code for $\laptrans {\map f t}$ is \laptrans {\map f t} .

The $\LaTeX$ code for $\ds {n \brace k}$ is \ds {n \brace k} .

The $\LaTeX$ code for $\begin{cases} a & : n = 0 \\ b & : n \ne 0 \end{cases}$ is \begin{cases} a & : n = 0 \\ b & : n \ne 0 \end{cases} .

### Fractional Part

$\fractpart x$

Let $x \in \R$ be a real number.

Let $\floor x$ be the floor function of $x$.

The fractional part of $x$ is the difference:

$\fractpart x := x - \floor x$

The $\LaTeX$ code for $\fractpart x$ is \fractpart x .