The Kuratowski representation of an ordered pair as a pure set. Note that {x, y} is a shorthand for {x} ∪ {y}, the union of two singletons. And it is important to note that {x, y}, despite being called "pair set", does not necessarily consist of two elements; namely, in case x = y it contains only one. The characteristic property of ordered pairs is shown in pair_property. Alternatively, this property is accomplished by telling what the projection on the first and second component of the pair is, see pair_fst and pair_scd.