Relations provide the means of comparing mathematical objects, such as sets or numbers. For infinite relations, this chapter considers a different method that works in the particular case of a relation on the set of real numbers ∅. It introduces partial order relations and equivalence relations. The chapter focuses on a function's behavior relative to individual values shifts to a consideration of its behavior relative to sets. Such considerations play a prominent role in higher mathematics courses, such as advanced calculus and real analysis. The chapter discusses arbitrary unions and intersections of sets and generalizes the special cases of these operations, such as finite unions and intersections. Applications to database queries are also discussed. The chapter addresses the utility of hash functions and tables. Functions are special kind of relation. Real polynomial functions and exponential functions are important examples of real functions.