The language of set theory is based on a single fundamental relationship called membership .

 The individual objects in a set are called the members or elements of the set. A set is identified uniquely by its members.

For example, R = {1, 2, 3} is the set R containing 1, 2, and 3 as its members.

A member is related to a set using the symbol , which means is an element of , is a member of , or belongs to . For set R = {1, 2, 3}, 1 R can be read, 1 is an element of R , 1 is a member of R , or 1 belongs to R . For set R , you also know 2 R and 3 R .

To identify objects not in a set use the symbol . It means is not an element of , is not a member of , or does not belong to . For set R = {1, 2, 3}, a possible example is 6 R , which is read, 6 is not an element of R .

A set must be defined properly so you can determine whether an object is a member of the set. There are several ways to do this including written description , roster method , and set notation .

 A is the set of natural numbers below 30 divisible by 5. B is the set of odd digits. C is the set of whole numbers. A = {5, 10, 15, 20, 25} B = {1, 3, 5, 7, 9} C = {0, 1, 2, 3, ...} A = { x |0 < x < 30, x divisible by 5} B = { x |0 < x < 10, x is odd} C = { x | x W}