nLab
Kuratowski pairs

Contents

Idea

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.

References

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