The concept of *Kuratowski pair* is one possible way of encoding the concept of an ordered pair in material set theory (say in the construction of Cartesian products): A pair of the form $(a,b)$ is represented by the set of the form $\{\{a\}, \{a,b\}\}$.

The main point is to cook up a definition whereby $(a, b) = (a', b')$ if and only if $a = a'$ and $b = b'$, where set equality may be verified via the axiom of extensionality. Obviously many such definitions are possible, but Kuratowski’s is a simple one.

- Wikipedia,
*Ordered pair - Kuratowski definition*

Last revised on May 8, 2017 at 20:06:34. See the history of this page for a list of all contributions to it.