Concept
Axiom of extensionality
Overview
The axiom of extensionality, also called the axiom of extent, is an axiom used in many forms of axiomatic set theory, such as the Zermelo–Fraenkel set theory. The axiom defines what a set is. Informally, the axiom means that the two sets A and B are equal if and only if A and B have the same members.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Related ideas
- Formal language
- First-order logic
- Parity (mathematics)
- Integer
- Intension
- Free variables and bound variables
- If and only if
- Zermelo–Fraenkel set theory
- John von Neumann
- Necessity and sufficiency
- Ernst Zermelo
- Oxford English Dictionary
- Logical biconditional
- Set (mathematics)
- Set theory
- Predicate (logic)
- Zermelo set theory
- Willard Van Orman Quine
- Russell's paradox
- Logic
- Frege's theorem
- Gottlob Frege
- Substitution (logic)
- Alfred Tarski
Place in the tradition
Part of First-order logic.