29.3 Injunction and adjunction are the closest types of boundary union possible respectively for an event with its part and for a pair of separated events. The geometry for events is four-dimensional, but in the three-dimensional analogue such a surface union for a pair of volumes would be the existence of a finite area of surface in common. [Note that spatial diagrams, such as the one above, are to some extent misleading in that they emphasise the spatial character of events at the expense of their temporal character. The temporal character is very far from being represented by an extra dimension producing an ordinary four-dimensional euclidean geometry.] 30. Abstractive Classes. 30.1 A set of events is called an 'abstractive class' when (i) of any two of its members one extends over the other, and (ii) there is no event which is extended over by every event of the set. The properties of an abstractive class secure that its members form a series in which the predecessors extend over their successors, and that the extension of the members of the series (as we pass towards the 'converging end' comprising the smaller members) diminishes without limit; so that there is no end to the series in this direction along it and the diminution of the extension finally excludes any assignable event. Thus any property of the individual events which survives throughout members of the series as we pass towards the converging end is a property belonging to an ideal simplicity which is beyond that of any one assignable event. There is no one event which the series marks out, but the series itself is a route of approximation towards an ideal simplicity of 'content.' The systematic use of these abstractive classes is the 'method of extensive abstraction.' All the spatial and temporal concepts can be defined by means of them. 30.2 One class of events—, say—is said to 'cover' another class of events—, say—when every member of a extends over some member of . If a be an abstractive class and covers , then must have an infinite number of members and there can be no event which is extended over by every member of . For any member of , however small, extends over some member of . The usual case of covering is when both classes, and , are abstractive classes; then each member of , the covering class, extends over the whole converging end of subsequent to the first member of which it extends over. 30.3 Two classes of events are called '-equal' when each covers the other. Evidently such classes cannot have a finite number of members. Inequality is a relation in which two abstractive classes can stand to each other. The relation is symmetrical and transitive, and every abstractive class is -equal to itself. [Note. Abstractive classes and the relation of 'covering' can be illustrated by spatial diagrams, with the same caution as to their possibly misleading character. Fig. 5.