Linked from

The 37 pages that link to Power set, each with the reason it gives.

• SetBroader topic: It gathers every possible subcollection of a set into one set.

• Set theoryBroader topic: The power-set operation creates larger sets and drives results about cardinality.

• Zermelo–Fraenkel set theoryRelated: The power-set axiom provides a central operation for constructing larger sets.

• Cartesian productRelated: A power set can be identified with the product of two-element membership choices.

• Georg CantorRelated: Cantor’s theorem compares a set’s size with the size of its power set.

• Continuum hypothesisRelated: Cantor's theorem makes the real numbers' cardinality equal to that of the natural numbers' power set.

• SubsetBroader topic: It gathers every set related to a given set by subsethood.

• Sigma-algebraNarrower topic: A sigma-algebra is a selected subcollection of this larger family.

• CardinalityRelated: Its cardinality is always greater than that of the original set.

• Empty setRelated: The empty set has exactly one subset: itself.

• Finite setRelated: A finite set with n elements has a power set with 2ⁿ elements.

• Sample spaceRelated: When every subset is an event, the event space is the sample space's power set.

• Cantor's theoremBroader topic: It is the set whose cardinality Cantor’s theorem compares with the original set.

• Lattice (order theory)Broader topic: Union and intersection give joins and meets for every pair of subsets.

• Cumulative hierarchyRelated: At each successor stage, taking a power set generates the next level.

• DiagonalizationRelated: The diagonal subset is formed by checking whether each element belongs to its corresponding listed subset.

• MonoidRelated: Under union, a power set forms a monoid whose identity is the empty subset.

• Second-order logicRelated: Under standard semantics, unary predicates range over subsets of the object domain.

• Cardinal numberRelated: Its cardinality always exceeds that of the original set.

• ElementBroader topic: Its elements are themselves sets built from elements of the original set.

• Least elementRelated: Ordered by inclusion, its empty subset is the least element.

• Set-builder notationRelated: Its membership condition says that each element is itself a subset of the original set.

• Transfinite recursionRelated: Recursive clauses often take values in power sets, especially when defining hierarchies of sets.

• Uncountable setRelated: The power set of the natural numbers is uncountable by Cantor's theorem.

• Minimal elementRelated: Ordered by inclusion, a power set makes the empty set the unique minimal element.

• Boolean ringRelated: With symmetric difference and intersection, a power set is a canonical Boolean ring.

• Membership relationRelated: Membership in a power set means being a subset of its underlying set.

• Axiom of Power SetBroader topic: The axiom guarantees this collection is itself a set.

• Von Neumann universeRelated: Taking power sets generates successor stages of the hierarchy.

• Schröder–Bernstein theoremRelated: Cantor's theorem uses power sets to show that cardinal sizes can strictly increase.

• Erdős–Rado theoremRelated: Colorings of pairs are functions defined on part of a power set.

• Venn diagramRelated: A diagram with n sets must account for all 2ⁿ membership combinations.

• Axiom of Empty SetRelated: The empty set’s power set contains exactly one subset, itself.

• Cardinality of the continuumRelated: The power set of the naturals has the continuum's cardinality.

• Dynkin systemNarrower topic: A Dynkin system is a subcollection of this larger family.

• Element of a setBroader topic: Its elements are sets, illustrating that sets can themselves be members.

• Greatest element and least elementRelated: Under inclusion, the empty set is least and the whole underlying set is greatest.