This chapter deals with a special type of relations on elements of two sets. A real relationship of children and mother is used as the brainstorming experiment to explain the function and types of functions such as one-to-one functions, onto functions, into functions, and bijective functions. Moreover, the particular examples support for the better understanding of applied aspects of the functions. It also focuses on the concepts of floor and ceiling function with examples. By considering the experiment of writing English words, this chapter explains the definitions of infinite sets, countable sets and related results with illustrations. The pigeonhole principle is enlightened by using the real examples of library systems in various institutions. Moreover, special examples are designed to understand the applications of this concept. Furthermore, discrete numeric functions are described with illustrations. This chapter concludes with the case studies, projects, and exercises to fill up the gap between theoretical concepts and their multifaceted applications.