power set

This term is used exclusively within the domain of set theory and discrete mathematics. It describes a specific operation that transforms a set into a larger set containing every possible combination of its elements. The resulting power set always has a cardinality of 2 raised to the power of the original set's size.

In a technical context, the power set is often denoted by P(S) or 2^S. It is a fundamental concept used to define topologies and explore the properties of infinite sets, such as Cantor's theorem, which proves that the power set of any set has a strictly greater cardinality than the set itself.