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:

$$(a,b)=(c,d)\iff a=b\text{ and }c=d,$$

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