In set theory, a **power set** (or powerset) is a set of all of the subsets of a given set. A power set is usually designated by *P*(S), where S is some set.

For example, suppose that *S* is the set { α, β, γ }. The power set of S, *P*(S), is therefore:

{ ∅, {α}, {β}, {γ}, {α, β}, {α, γ}, {β, γ}, {α, β, γ} }

Note that the power set always includes the empty set, ∅ or {}. This is because the empty set is a subset of every set.