Basics of Sets

The concepts of set and subset, the principle of extensionality, the empty set, union and intersection of sets

A set is a collection of objects. It can be thought of as the container of those objects and, together, as what gives them unity.

Membership, order, listing

The objects that belong to a set are called elements or members of the set. The symbol ∈ indicates that an object belongs to a set. For example, to say that the object x belongs to the set A, we write:

Instead, to indicate that x does not belong to A, we write:

For sets consisting of a few elements, it is convenient to list the elements of the set. Usually, the list of elements, separated by commas, is enclosed in curly brackets and preceded by the set’s name, denoted by a capital letter, and by the equal sign. For example, if A is the set of perfect squares less than 50, then we will write: