Full Idea
Axiom of Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x). That is, there is a set which contains zero and all of its successors, hence all the natural numbers. The principal of induction rests on this axiom.
Gist of Idea
Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x)
Source
Kenneth Kunen (Set Theory [1980], §1.7)
Book Reference
Kunen,Kenneth: 'Set Theory: Introduction to Independence Proofs' [North-Holland 1980], p.19
Related Idea
Idea 15931 The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine]