Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Power set

In mathematics, the power set (or powerset) of a set S is the set of all subsets of S, including the empty set and S itself. In axiomatic set theory (as developed, for example, in the ZFC axioms), the existence of the power set of any set is postulated by the axiom of power set. The powerset of S is variously denoted as P(S), 𝒫(S), P(S), P ( S )…

Measurement, Properties & Power object

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Research this topic

Explore the main themes, entities and connections around Power set. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Key facts & relationships

High-confidence facts extracted from structured source data. Use them as anchors for further research.

Field
Set theory
Statement
The power set is the set that contains all subsets of a given set.
Type
Set operation

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

Properties

Representing subsets as functions

Relation to binomial theorem

Recursive definition

Power object

Functors and quantifiers

Bibliography

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

Map overview Semantic statistics

Power set

Nodes83
Edges82
Triples61
Avg. degree1.98
Density0.024096
Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Power set

Top relations

related to Bibliography · 27
Power set → Archived, Devlin, Eric, Formal Languages, Fundamentals, Geometry, Halmos, Ieke, ISBN, Keith, Logic, Mac Lane, Moerdijk, Naive, Nostrand Company, Paul, Retrieved, Saunders, Sheaves, Springer-Verlag
related to Functors and quantifiers · 9
Power set → Elsewhere, Formally, In, Pf, Set, That, The, There, This
related to Properties · 6
Power set → Cantor's, Cardinality, If, In, The, This
related to Representing subsets as functions · 6
Power set → As, First, In, Neumann, This, XY
related to Power object · 4
Power set → Boolean, From, So, The
related to External links · 3
Power set → Algorithm, PlanetMath, Power
related to Relation to binomial theorem · 2
Power set → For, The
Field · 1
Power set → Set theory
Statement · 1
Power set → The power set is the set that contains all subsets of a given set.
Symbolic statement · 1
Power set → x ∈ .mw-parser-output .mathcal{font-family:"Lucida Calligraphy","Monotype Corsiva","URW Chancery L","Apple Chancery","Tex Gyre Chorus",cursive,serif}P(S) ⟺ x ⊆ S

Important terminology Word statistics

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

set power subsets algebra theory functions cardinality example elements functor number operations subalgebras empty denoted 2s called sets theorem object

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Power setFieldSet theory1.00infobox
Power setStatementThe power set is the set that contains all subsets of a given set.1.00infobox
Power setSymbolic statementx ∈ .mw-parser-output .mathcal{font-family:"Lucida Calligraphy","Monotype Corsiva","URW Chancery L","Apple Chancery","Tex Gyre Chorus",cursive,serif}P(S) ⟺ x ⊆ S1.00infobox
Power setTypeSet operation1.00infobox
Power setrelated to BibliographyDevlin0.60section
Power setrelated to BibliographyKeith0.60section
Power setrelated to BibliographyFundamentals0.60section
Power setrelated to BibliographyUniversitext0.60section
Power setrelated to BibliographySpringer-Verlag0.60section
Power setrelated to BibliographyISBN0.60section
Power setrelated to BibliographyZbl0.60section
Power setrelated to BibliographyHalmos0.60section

Related concept clusters Concept neighborhoods

These clusters group vocabulary that occurs around closely connected concepts in the source material.

    Connections between topic areas Semantic bridges

    Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

    Min side: 3
    For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.