\begin{definition}[Definition:Braces]
'''Braces''' is the name given to the pair of '''curly brackets''':
:$\set {\cdots}$
These are conventionally used mostly for:
:$(1): \quad$ Set delimiters, to membership of sets and classes.
:$(2): \quad$ the fractional part of a real number:
::::$\fractpart x := x - \floor x$
:::where $\floor x$ denotes the floor of $x$.
:$(3): \quad$ Karamata notation for the Stirling numbers of the second kind:
::::$\ds {n \brace k}$
On {{ProofWiki}}, which implements the $\LaTeX$ mathematical markup language, '''braces''' are also used to delimit arguments to $\LaTeX$ commands.
Category:Definitions/Language Definitions
\end{definition}