What is a relation in mathematics?

In mathematics, a relation refers to a correspondence or association between two sets of values, typically represented by two variables. This concept allows us to understand how one variable may depend on or interact with another. For example, in the case of ordered pairs (x, y), where x and y are elements from two different sets, a relation describes how each x-value corresponds to a specific y-value.

Relations can be categorized further into functions, but they are a broader concept that encompasses any pair of input and output values, not only those that satisfy the criteria of a function (such as having only one output for each input). Thus, when we say that a relation is a correspondence between two variables, we recognize it as a foundational idea that leads into further explorations in mathematics, such as functions, equations, and graphs.