# Subset

From Citizendium

In set theory, a **subset** of a set *X* is a set *A* whose elements are all elements of *X*: that is, , denoted . The empty set Ø and *X* itself are always subsets of *X*. The containing set *X* is a **superset** of *A*. The relation between the subset and the superset is **inclusion**, and the **inclusion map** is the map from *A* → *X* which is the identity on *A*.

The power set of *X* is the set of all subsets of *X*.