ABSTRACT
This chapter discusses the limits of functions, limit inferior, and limit superior of functions. It reviews locally defined functions and a poorly behaved function. The sequence limits are provided for sequences with infinitely many rational values and finitely many irrational values which will have a limit. The chapter describes the case of sequences with infinitely many irrational values and finitely many rational values. It provides an example of a function where the cluster point set is always two values. Limits of functions and continuity of functions are pointwise concepts, and not interval based concepts. Continuity for all points in an entire interval should have important consequences. One can construct really interesting examples of functions which are infinitely differentiable but which are nonzero on any chosen finite interval.
