Suppose that I have relation f:X↔Y, where f is a subset of X×Y.
Note that for x in X, it might relate to multiple elements in Y.
Similarly, for y in Y, it might relate to multiple elements in X.
Does anybody know what the number of elements in one set (X or Y) an element in the other set (Y or X) can be related to is called?
The only thing that comes to me is to interpret your relation as a directed graph.
Then $(x,y)\in f$ means “there is an edge from $x$ to $y$” and the size of the subset of elements of the form $(x,\cdot)$ is called the out-degree of $x$ and the size of the set of elements of the form $(\cdot,y)$ is called the in-degree of $y$.
It’s possible that people who do pure relation theory also have a term for it, but I don’t know what it is.