Volume 1 / Part 1 — *36. RELATIONS WITH LIMITED FIELDS.
Reading edition
*36. RELATIONS WITH LIMITED FIELDS.
Summary of *36.
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:
*36·01.
We thus have
*36·13.
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:
*36·25.
*36·29.
*36·3.
*36·33.
*36·01.
*36·11.
*36·13.
The following propositions are obtained from those of *35 by means of *36·11, which, as it is used in each case, is not referred to again.
*36·2.
*36·201.
*36·202.
*36·203.
*36·21.
*36·22.
Dem.
*36·23.
*36·24.
*36·241.
*36·25.
Dem.
*36·26.
*36·27.
*36·28.
*36·29.
*36·3.
Dem.
*36·31.
*36·32.
*36·33.
*36·34.
*36·35.
*36·4.
Dem.