\begin{definition}[Definition:Ordered Pair/Kuratowski Formalization]
The definition of a set does not take any account of the order in which the elements are listed.
That is, $\set {a, b} = \set {b, a}$, 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:
:$\tuple {a, b} := \set {\set a, \set {a, b} }$
This formalization justifies the existence of ordered pairs in Zermelo-Fraenkel set theory.
\end{definition}