(called the end-points), and (ii) is such that no selection of the event-particles which it covers can be the complete set of event-particles covered by another simple abstractive class, provided that the selection comprises
and
and does not comprise all the event-particles covered by
. The condition (i) secures that a linear abstractive class converges to an element of higher complexity than an event-particle; and the condition (ii) secures that it has the linear type of continuity.
A 'linear prime' is an abstractive class which is prime in respect to the formative condition of (i) being covered by an assigned linear abstractive class covering two assigned end-points and (ii) being itself a linear abstractive class covering the same assigned end-points. This formative condition is evidently regular for primes.
A 'route' is the abstractive element deduced from a linear prime. The two assigned event-particles which occur as end-points in the definition of the linear prime from which a route is deduced are called the 'end-points' of that route. A route is said to lie between its end-points.
38.2 A route is a linear segment, straight or curved, between two event-particles, co-momental or sequent. There are an indefinite number of routes between a given pair of event-particles as end-points. A route will cover an infinite number of event-particles in addition to its end-points. The continuity of events issues in a theory of the continuity of routes.