From my book: "We agree that there is exactly one 0-tuple in [set] X, and we designate it by ( ). A 0-ary function from X to Y is then completely determined by its value for the argument ( ). We shall identify the function with this value. This means that a 0-ary function from X to Y is simply an element of Y." I don't understand the reasoning behind the second sentence. How does a function even work on an empty sequence? Edit: I may as well tack this on here. "universe" and "individuals" are undefined terms, right? I've never seen them defined, not formally anyway, and they seem to be basic concepts.