ABSTRACT
Two series s, s' are said to be correlated when there is a one-one relation R coupling every term of s with a term of s' , and vice versâ, and when, if x, y be terms of s, and x precedes y, then their correlates x' , y' in s' are such that x' precedes y' . Two classes or collections are correlated whenever there is a oneone relation between the terms of the one and the terms of the other, none being left over. Thus 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 will be explained hereafter. In order to distinguish these cases, it will be well to speak of the correlation of classes as correlation simply, and of the correlation of series as ordinal correlation. Thus whenever correlation is mentioned without an adjective, it is to be understood as being not necessarily ordinal. 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.
