Two relations R and R' are said to be ordinally similar, if a one-one relation holds between the members of the two fields of R and R', such that if x and y are any two members of the field of R, such that x has the relation R to y, and if x' and y are the correlates in the field of R' of x and y, then in all such cases x has the relation R' to y', and conversely, interchanging the dashes on the letters, i.e.

For a one-one relation can be established between the members of a and a by the simple process of correlating each member of a with itself.

Two classes between which a one-one relation exists have the same cardinal number and are called cardinally similar; and the cardinal number of the class a is a certain class whose members are themselves classes - namely, it is the class composed of all those classes for which a one-one correlation with a exists.