ABSTRACT
In the theory of continuity and the ordinal theory of infinity, the problems that arise are not specially concerned with numbers, but with all series of certain types which occur in arithmetic and geometry alike. It is a singular fact that, in proportion as the infinitesimal has been extruded from mathematics, the infinite has been allowed a freer development. Two series may be correlated as classes without being correlated as series; for correlation as classes involves only the same cardinal number, whereas correlation as series involves also the same ordinal type—a distinction whose importance. Correlated classes will be called similar; correlated series will be called ordinally similar; and their generating relations will be said to have the relation of likeness. The chapter aims to understand a distinction of great importance, namely that between self-sufficient or independent series, and series by correlation.
