ABSTRACT
This chapter reviews what continuity means for a function, and describes continuity at a point and careful continuity at a point. It discusses uniform continuity based on an interval and provides a set of examples for describing the uniform continuity. The set of examples is provided on open intervals using two different functions. The first function is not uniformly continuous and the second function is uniformly continuous. The concept of uniform continuity is described using illustrative examples from differentiation. The chapter describes the addition of uniformly continuous functions. The addition is considered as uniformly continuous based on a certain preset criteria.
