# 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 OrderedPair 2013-03-22 11:48:53 2013-03-22 11:48:53 djao (24) djao (24) 9 djao (24) Definition msc 03-00 msc 70A05 msc 70G99