Full Idea
The Axiom of Pairing says that for all sets x and y, there is a set z containing x and y, and nothing else. In symbols: ∀x∀y∃z∀w(w ∈ z ↔ (w = x ∨ w = y)).
Gist of Idea
Axiom of Pairing: for all sets x and y, there is a set z containing just x and y
Source
A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
Book Reference
George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.52
A Reaction
See Idea 10099 for an application of this axiom.
Related Idea
Idea 10099 The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}} [George/Velleman]