One of the symbols 
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).
