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 ,
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, (Harary 1994, pp. 91, 93, and 118119).