ABSTRACT
The conception of a “limit” is one of which the importance in mathematics has been found continually greater than had been thought. The whole of the differential and integral calculus, indeed practically everything in higher mathematics, depends upon limits. There are various forms of the notion of “limit,” of increasing complexity. Cantor defines a series as “perfect” when all its points are limiting-points and all its limiting-points belong to it. In view of the fundamental importance of motion in applied mathematics, as well as for other reasons, it will be well to deal briefly with the notions of limits and continuity as applied to functions.
