Given two (possibly infinite) cardinal numbers |X|, |Y|, where X, Y are sets, it is possible to define sums, products, and powers. The sum |X| + |Y| is defined as |X⊔Y|, the cardinality of the disjoint union. The product |X||Y| is defined as |X×Y|, the cardinality of the Cartesian product. The power |X|^|Y| is defined as the cardinality of the set of functions from Y to X. In particular, 2^|Y| is the cardinality of the power set of Y. All these definitions are theorems for finite sets, so it makes sense to extend these definitions to infinite sets. Cantor showed that 2^|ℕ| = |ℝ|. See also Cantor-Schröder-Bernstein theorem, continuum hypothesis.