Continuous Functions - Real Analysis | Lecture 11

In this lecture we introduce the precise definition of a continuous function. We will see that it is closely related to the precise definition of a limit from the previous lecture, and we make this rigorous with the first result of the lecture. With the relationship between continuity and the limit, we are then able to introduce the Sequential Criterion of Continuity which poses the condition for continuity of a function at a point in terms of convergent sequences. We illustrate our results with a number of examples that increase in difficulty.

This course is taught by Jason Bramburger.