>>11251452you seem like you dont care about an answer and just want to affirm your own ideas, but i will give you an answer anyway.
a function is defined in the following way. Let G be the set of pairs with one element from set A, and the other from set B. A function f from A to B is a set if pairs in G such that if x is in an element of f, and x is in A, then x is not in any other pair in f.
the point is to define a correspondence which labels elements of B using elements of A. this is a very general concept. what you are calling a multifunction is just a function whose output set is a set of all tuples with no specific length.
