we define a set to be any unordered collection of objects, e.g., is a set. if is an object, we say that is an element of or if lies in the collection; otherwise we say that . for instance, but .
let be a set. for any object , and any object , suppose we have a statement pertaining to and , such that for each there is at most one for which is true. then there exists a set , such that for any object ,