# Ordered Pair/Kuratowski Formalization/Warning

The weakness of the Kuratowski formalization of the ordered pair shows up when $a = b$:
 $\displaystyle \tuple {a, a}$ $=$ $\displaystyle \set {\set a, \set {a, a} }$ Definition of Kuratowski Formalization of Ordered Pair $\displaystyle$ $=$ $\displaystyle \set {\set a, \set a}$ Definition of Uniqueness of Set Elements $\displaystyle$ $=$ $\displaystyle \set {\set a}$ Definition of Uniqueness of Set Elements
Thus the ordered pair degenerates into the set $\set {\set a}$.