You are here
Home ›axiom of power set
Primary tabs
axiom of power set
The axiom of power set is an axiom of Zermelo-Fraenkel set theory which postulates that for any set there exists a set , called the power set of , consisting of all subsets of . In symbols, it reads:
In the above, is defined as . By the extensionality axiom, the set is unique.
The Power Set Axiom allows us to define the Cartesian product of two sets and :
The Cartesian product is a set since
We may define the Cartesian product of any finite collection of sets recursively:
Synonym:
power set axiom, powerset axiom, axiom of powerset
Type of Math Object:
Axiom
Major Section:
Reference
Mathematics Subject Classification
03E30 Axiomatics of classical set theory and its fragments- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)
- Other useful stuff
Recent Activity
Jun 15
new question: Sorry to steal a few minutes of your time for this question, but i honestly don't know what else to do. by Whrazithar
new question: equality of the determinants of submatrices of an orthogonal matrix by ismayli
Jun 11
new correction: Typo by suitangi
Jun 2
new question: Creating another set with same cardinality. by hkkass
Jun 1
new image: ProblemOneRevised by unlord
new Education: Chapter II by rspuzio
May 31
new collection: The Calculus by Davis and Brenke by rspuzio
new question: Proofs by weixifan
new question: Summation Integration Question by trevor.nickle
May 27
new correction: typo+finite measure hypothesis by Filipe
new question: Sorry to steal a few minutes of your time for this question, but i honestly don't know what else to do. by Whrazithar
new question: equality of the determinants of submatrices of an orthogonal matrix by ismayli
Jun 11
new correction: Typo by suitangi
Jun 2
new question: Creating another set with same cardinality. by hkkass
Jun 1
new image: ProblemOneRevised by unlord
new Education: Chapter II by rspuzio
May 31
new collection: The Calculus by Davis and Brenke by rspuzio
new question: Proofs by weixifan
new question: Summation Integration Question by trevor.nickle
May 27
new correction: typo+finite measure hypothesis by Filipe


