Full Idea
Axiom of Infinity: There exists a set containing the empty set and the successor of each of its elements.
Gist of Idea
Infinity: There exists a set of the empty set and the successor of each element
Source
Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
Book Reference
Clegg,Brian: 'Infinity' [Robinson 2003], p.206
A Reaction
This is rather different from the other axioms because it contains the notion of 'successor', though that can be generated by an ordering procedure.
Related Idea
Idea 15931 The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine]