more from Brian Clegg

### Single Idea 10878

#### [catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V]

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]**