Kuratowski pairs



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)(a,b) is represented by the set of the form {{a},{a,b}}\{\{a\}, \{a,b\}\}.

The main point is to cook up a definition whereby (a,b)=(a,b)(a, b) = (a', b') if and only if a=aa = a' and b=bb = 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.


Last revised on May 8, 2017 at 16:06:34. See the history of this page for a list of all contributions to it.