Is there an ordered pair function which sometimes returns a set with more than two elements?
There are many set-theoretic implementations of ordered pairs. In all of the definitions I have seen, ordered pairs always have, as sets, either one element or two elements. That raises the question, is there an ordered pair function $OP$ such that for at least one pair of sets $x$ and $y$, $OP(x,y)$ is a set with three or more elements?
The Quine-Rosser pairing function has this property: $\langle x,y\rangle_{\mathsf{QR}}$ is the union of sets related to $x$ and $y$ themselves, and so will generally have more than two elements.