Definition:Ordered Pair/Kuratowski Formalization

Definition
The definition of a set does not take any account of the order in which the elements are listed.

That is, $\left\{{a, b}\right\} = \left\{{b, a}\right\}$, and the elements $a$ and $b$ have the same status - neither is distinguished above the other as being more "important".

The concept of an ordered pair can be formalized by the definition:


 * $\left({a, b}\right) = \left\{{\left\{{a}\right\}, \left\{{a, b}\right\}}\right\}$

This formalization justifies the existence of ordered pairs in Zermelo-Fraenkel set theory.

Also see

 * Equivalence of Definitions of Ordered Pair

This formalization was established in collaboration with.