1. It seems most convenient, in virtue of the well-established pedagogic maxim that “algebraic subjects should, as far as possible, be introduced as generalisations of known principles in Arithmetic,” to base our teaching of limits and convergence upon the arithmetic theory of “Approximations,” with which all scholarship candidates are familiar as a practical instrument.

The formal definition of a limit by means of a sequence is usually found by the beginner very hard to understand, but if presented from the point of view of approximations it is less difficult.