There are several ways to look at sets. Two sets (or more) are considered identical if, and only if, they have the same collection of objects or entities. This is a principle known as extensionality. For example, the set {a, b, c} is considered to be the same as set {a, b, c}, of course, because the elements are the same; the set {a, b, c} and the set {c, b, a} are also the same, even though they are written in a different order.

It becomes more complex when sets are elements of other sets, so it is important to note the position of the brackets. For example, the set {{a, b}, c} is distinct from the set {a, b, c} (note that the brackets differ); in turn, the set {a, b} is an element of the set {{a, b}, c}. (It is a set included between the outside brackets.)

Another example that shows how sets are interpreted includes the following: If B is the set of real numbers that are solutions of the equation x² = 9, then the set can be written as B = {x: x² = 9}, or B is the set of all x such that x² = 9. Thus B is {3, -3}.