Concept
Axiom of infinity
Overview
In axiomatic set theory and the branches of mathematics and philosophy that use it, the axiom of infinity is one of the axioms of Zermelo–Fraenkel set theory. It guarantees the existence of at least one infinite set, namely a set containing the natural numbers. It was first published by Ernst Zermelo as part of his set theory in 1908.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Related ideas
- First-order logic
- Philosophy
- Infinite set
- Zermelo–Fraenkel set theory
- Ernst Zermelo
- Mathematics
- Mathematical induction
- Natural number
- Power set
- Set theory
- Zermelo set theory
- Second-order logic
- Second-order arithmetic
- Axiom of extensionality
- Von Neumann–Bernays–Gödel set theory
- Cardinality
- Existential quantification
- Axiom
- Empty set
- Set-theoretic definition of natural numbers
Place in the tradition
Part of Logicism.