ABSTRACT

Here we take our first real examination of the central ideas of limits and continuity. A strong effort is made to get the reader to understand the difference between pointwise continuity and uniform continuity. Examples that are counterintuitive are presented as well as basic results such as, the continuous image of a compact set is compact and the continuous image of a connected set is connected. Continuity of monotone and inverse functions is discussed. Different types of discontinuities are mentioned.