Full Idea
The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}}. The existence of this set is guaranteed by three applications of the Axiom of Pairing.
Gist of Idea
The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}}
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.56
A Reaction
See Idea 10100 for the Axiom of Pairing.
Related Idea
Idea 10100 Axiom of Pairing: for all sets x and y, there is a set z containing just x and y [George/Velleman]