ABSTRACT
This chapter discusses the question is this: Can we ultimately distinguish open from closed series, and if so, in what does the distinction consist? Every series being generated by a transitive asymmetrical relation between any two terms of the series, a series is open when it has either no beginning, or a beginning which is not arbitrary; it is closed when it has an arbitrary beginning. In all cases of closed series, though there may be an asymmetrical one-one relation if the series is discrete, the transitive asymmetrical relation must be one involving one or more fixed terms in addition to the two variable terms with regard to which it generates the series. The series acquires a definite order, but one in which, as in all closed series, the first term is arbitrary.
