The preceding theorem shows how the general notions, referring to classes, are related to the corresponding ones, restricted to sets. If we wish to extend the above relations to the other concepts of set theory like, for instance, the notions of ordered pair, function, ordinal number, and cardinal number, it is clear that several modifications must be made in the general definitions (borrowed from [13]) or in the definitions of the restricted notions (adapted from [9], appendix).