ABSTRACT
In this chapter, the authors define continuous function, give some examples, and study some of their elementary properties. They develop some of the elementary properties of continuous functions. The authors show that the sum of two continuous functions and the product of a continuous function by a real number are continuous. They discuss linear transformations. The authors argue that continuous functions can be combined in various ways to obtain new continuous functions. For example, the sum and product of continuous functions are again continuous. The authors also define continuity for functions between Euclidean spaces. They examine the notion of a convergent sequence in a Euclidean space. Their definition is the obvious extension of the corresponding notion for real numbers.
