 Axiom of infinity

The axiom asserts the existence of a set containing the empty set and closed under the successor operation $x\mapsto x\cup \{x\}$:In Zermelo–Fraenkel set theory, this supplies a set from which the set of natural numbers is constructed.

The Axiom of Infinity is one of the axioms of set theory, particularly in the context of Zermelo-Fraenkel set theory (ZF), which is a foundational system for mathematics. The Axiom of Infinity asserts the existence of an infinite set. Specifically, the axiom states that there exists a set \( I \) such that: 1. The empty set \( \emptyset \) is a member of \( I \).