A subset is a set whose elements are all contained within another set.
If every element of A is also in B, then A is a subset of B, written A β B. A proper subset (A β B) means A β B but A β B. The empty set β is a subset of every set. Every set is a subset of itself. The power set of a set is the collection of all its subsets. Subset relationships are often visualized using Venn diagrams.
The subset concept was formalized by Georg Cantor in his set theory work (1870s). The notation β was introduced by Ernst SchrΓΆder in 1890. Subset relationships are fundamental to the axiomatic foundation of mathematics.