Principia mathematica, vol. 1 (of 3)

In this number we are concerned with the special case in which the same limitation is imposed upon the domain and the converse domain of a relation. In this case, the same result is achieved by imposing the limitation on the field. It is convenient to be able to regard as a descriptive function of or of , which we secure by the notation , whence, as will be explained in *38, and will both mean . If is a serial relation, and , "" will stand for "the terms of arranged in the order determined by ," or, as we may call it briefly, " in the -order." is defined as follows:

Most of the propositions concerning demand that should have some at least of the characteristics of a serial relation. Hence the propositions concerning which can be given in the present number are, for the most part, not the most useful propositions concerning . The most useful propositions in the present number are the following: