ABSTRACT
This chapter turns our attention to functions whose domains may be intervals or other subsets of R. It considers questions of closeness, convergence, and shape (or topology) of the underlying domain and image of the function. The initial task will be to precisely capture the limiting behavior of f(x) as the inputs x are chosen increasingly and arbitrarily close to an accumulation point of the domain. The main focus is to develop what it means for a function to be continuous. Just as there were multiple ways to define the limit of a function at a point, there are multiple ways to define what it means for a function to be continuous at a point.
