Continuity

Abstract

A crucial use of the idea of limit is to separate out a class of functions to study: exactly those whose value at a point coincides with the limit at that point. This is a useful class because it is relatively easy to study and it includes many familiar and useful functions.¹

Of course, they are familiar because we’ve swept the others under the rug. But more seriously, they were possible to study in the days before computers, and are used to model all sorts of physical phenomena.