Braces are the opening and closing curly delimiters 
and 
used in many different contexts in mathematics. Braces are used
1. To denote grouping of mathematical terms, usually as the outermost delimiter in a complex expression such as ![{a+b[c+d(e+f)]}](/images/equations/Brace/Inline3.svg)
,
2. To delineate a set, as in 
,
3. Using a left brace only, to denote different cases for an expression, such as
 |
(1)
|
4. Using a single horizontal underbrace, to indicate the number of items in a list with not all elements shown explicitly, as in 
.
5. As an alternate notation for the fractional part function, 
.
6. As an alternate notation for the ceiling function, ![{x}=[x]](/images/equations/Brace/Inline7.svg)
(Harary 1994, pp. 91, 93,
and 118-119).
In graph theory, the term brace also denotes a brace graph (Feng and Zhou 2026).
