 There is exactly one Boolean algebra of cardinality every finite power of 2, and it is isomorphic to the Boolean algebra of a power set \(2^X\) of that cardinality under the set operations of union, intersection, and complement relative to \(X\). Hence all finite Boolean algebras have cardinality a power of 2. This situation changes with infinite Boolean algebras; in particular countable Boolean algebras exist. One such is the free Boolean algebra on countably many generators, which is the only countable atomless Boolean algebra. The finite and cofinite (complement of a finite set) subsets of the set \(N\) of natural numbers form a subalgebra of the powerset Boolean algebra \(2^N\) not isomorphic to the free Boolean algebra, but it has atoms, namely the singleton sets.