What Is a Set?

A set is a well-defined collection of distinct objects — 'well-defined' meaning there is a clear rule that lets us decide, for any object, whether it belongs to the collection or not. The individual objects in a set are called its elements or members, written $a \in A$ to mean '$a$ is an element of the set $A$'. Two things must hold together: the membership rule must be unambiguous (a collection like 'the most talented singers' isn't a set, sinc …