A definite event-particle is defined in reference to a definite punct in the following manner: Let the condition {sigma} mean the property of covering all the abstractive elements which are members of that punct; so that an abstractive set which satisfies the condition {sigma} is an abstractive set which covers every abstractive element belonging to the punct.

Then the definition of the event-particle associated with the punct is that it is the group of all the {sigma}-primes, where {sigma} has this particular meaning.
It is evident that--with this meaning of {sigma}--every abstractive set equal to a {sigma}-prime is itself a {sigma}-prime.

Accordingly an event-particle as thus defined is an abstractive element, namely it is the group of those abstractive sets which are each equal to some given abstractive set.

If we write out the definition of the event-particle associated with some given punct, which we will call {pi}, it is as follows: The event-particle associated with {pi} is the group of abstractive classes each of which has the two properties (i) that it covers every abstractive set in {pi} and (ii) that all the abstractive sets which also satisfy the former condition as to {pi} and which it covers, also cover it.
An event-particle has position by reason of its association with a punct, and conversely the punct gains its derived character as a route of approximation from its association with the event-particle.

These two characters of a point are always recurring in any treatment of the derivation of a point from the observed facts of nature, but in general there is no clear recognition of their distinction.
The peculiar simplicity of an instantaneous point has a twofold origin, one connected with position, that is to say with its character as a punct, and the other connected with its character as an event-particle.
The simplicity of the punct arises from its indivisibility by a moment.
The simplicity of an event-particle arises from the indivisibility of its intrinsic character.