Set

A set is an object $A$ for which it makes sense to ask, for any object $x$, whether $x \in A$ ("$x$ is an element of $A$").

In axiomatic set theory (e.g. ZFC ), “set” and the membership relation $\in$ are taken as primitive, and other basic notions—such as subsets and the empty set —are defined using $\in$.

Examples:

• $\{1,2,3\}$ is the set whose elements are $1,2,3$.
• $\emptyset$ is the set with no elements.
• $\mathbb{Z}$ is the set of integers.