more from A.George / D.J.Velleman

### Single Idea 10100

#### [catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II]

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]**