Symbols:Brackets/Braces
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
.