In dealing with the potencies of sets, we regard the individual elements (points) of the sets as indistinguishable, or more properly as not distinguished from one another, so that potency enables us to compare sets, regarded as troops in uniform, with one another. The idea embodied in content is totally different: here the individual points are no longer to be regarded as indistinguishable, indeed certain of the points, viz. the semiexternal points of the black intervals, seem to play a different rôle from the others. The distinguishing property, however,—viz. the relative position of the points—was dependent for its very definition on the existence of the underlying straight line as fundamental region. This will all become still more evident when we come to deal with sets in the plane and higher space. Content is not, like potency, a property of the set per se, but a property of the set with respect to the fundamental region.

Order is another property of the set per se, but in the determination of the order each individual again bears its own share. In dealing with order we come first to consider the mutual relations of the individuals as such among themselves, and the question arises how are these mutual relations to be characterised, what can we adopt as a measure of order? As before the measurement of order will be made to depend on (1, l)-correspondence between a given set and a set of known standard form, the characteristic property being maintained, the orders of these standard sets are called the ordinal types.