Another class of relations that is of the greatest use is the class of one-many relations, i.e. relations which at most one term can have to a given term. Such are father, mother, husband (except in Tibet), square of, sine of, and so on. But parent, square root, and so on, are not one-many. It is possible, formally, to replace all relations by one-many relations by means of a device. Take (say) the relation less among the inductive numbers. Given any number greater than 1, there will not be only one number having the relation less to , but we can form the whole class of numbers that are less than . This is one class, and its relation to is not shared by any other class. We may call the class of numbers that are less than the "proper ancestry" of , in the sense in which we spoke of ancestry and posterity in connection with mathematical induction. Then "proper ancestry" is a one-many relation (one-many will always be used so as to include one-one), since each number determines a single class of numbers as constituting its proper ancestry. Thus the relation less than can be replaced by being a member of the proper ancestry of. In this way a one-many relation in which the one is a class, together with membership of this class, can always formally replace a relation which is not one-many. Peano, who for some reason always instinctively conceives of a relation as one-many, deals in this way with those that are naturally not so. Reduction to one-many relations by this method, however, though possible as a matter of form, does not represent a technical simplification, and there is every reason to think that it does not represent a philosophical analysis, if only because classes must be regarded as "logical fictions." We shall therefore continue to regard one-many relations as a special kind of relations.