Abstract
This chapter discusses more gradual or continuous change. It focuses on the functions whose domain is the set of real numbers or else some subset of this, such as, an open or closed interval. The co-domain of these functions would also be the set of real numbers. They are described as functions of a real variable. The concept of an increasing or decreasing function is analogous to that of an increasing or decreasing sequence. Commonly occurring functions are invariably continuous except sometimes at a few isolated points. However, the property of continuity would only be of use if one is able to prove that some of those properties of a function that he would expect it to possess from the fact that it is continuous are valid.
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