A set is a collection of things usually numbers. The axioms of set theory imply the existence of a set-theoretic universe so rich that all mathematical objects can be construed as sets 1. Example 1 Let X 1 2 3 4 5 6 and Y 1 2.
The elements that make up a set can be any kind of things people letters of the alphabet or mathematical objects such as numbers points in space lines or other geometrical shapes algebraic constants and variables or even other sets.
The individual objects in a set are called the members or elements of the set. A b c d e f etc. A set may be defined by a membership rule formula or by listing its members within braces. A set is a well-defined collection of distinct objects.