and a finite cardinal is constant and infinite: from a quantitative point of view, finite numbers get no nearer to
as they grow larger. What makes
the limit of the finite numbers is the fact that, in the series, it comes immediately after them, which is an ordinal fact, not a quantitative fact.
There are various forms of the notion of "limit," of increasing complexity. The simplest and most fundamental form, from which the rest are derived, has been already defined, but we will here repeat the definitions which lead to it, in a general form in which they do not demand that the relation concerned shall be serial. The definitions are as follows:—
The "minima" of a class
with respect to a relation
