What is a relation in mathematical terms?

A relation in mathematical terms is defined as a set of ordered pairs, which can be composed of elements from two sets. Each ordered pair consists of a first element and a second element, often representing a connection or correspondence between the two values. This definition is foundational in the study of functions, where relations are used to express how one quantity may depend on another, such as in coordinates on a graph.

In contrast, a mere collection of random values lacks the structure that defines a relation, as it does not specify any pairing or association among the elements. A strict linear equation describes a specific relationship between variables, but by itself does not encapsulate the broader concept of a relation, which can include various forms of connections beyond just linearity. A variable dependent on another variable describes a relationship but does not encompass the full definition of what constitutes a relation as a whole, since it focuses solely on dependence rather than the more general concept of ordered pairs.