The elements of a set are enumerated within a pair of curly brackets as shown in this example.
Instead of listing all the elements, we can represent a set in the set-builder notation specifying some common properties satisfied by the elements. Thus the set represents the set . We read '' as 'all such that'. Particularly, if a set is infinite having infinite number of elements or listing all the elements of the set is cumbersome, such a representation is useful.
If an element x is a member of the set A, we write . If x is not a member of A, we write . In the above example, and .
The null set or empty set is the set that does not contain any element. A null set is denoted by .
is a set and 
are its elements. 
represents the set 
. We read '
' as 'all 
. If x is not a member of 
. In the above example, 
and 
.
.