ordered pair

For any sets a and b, the ordered pair (a,b) is the set {{a},{a,b}}.

The characterizing property of an ordered pair is:

(a,b)=(c,d)a=b and c=d,

and the above construction of ordered pair, as weird as it seems, is actually the simplest possible formulation which achieves this property.

Title ordered pair
Canonical name OrderedPair
Date of creation 2013-03-22 11:48:53
Last modified on 2013-03-22 11:48:53
Owner djao (24)
Last modified by djao (24)
Numerical id 9
Author djao (24)
Entry type Definition
Classification msc 03-00
Classification msc 70A05
Classification msc 70G99