What do you call a set of ordered pairs where the first component corresponds to an element of one set and the second component to an element of another?

A set of ordered pairs where the first component corresponds to an element of one set and the second component corresponds to an element of another set is referred to as a relation. This concept is foundational in mathematics, particularly in the study of sets and their relationships.

A relation can be defined between two sets, say Set A and Set B, where each element from Set A is paired with an element from Set B. The ordered pairs are written in the form (a, b), where 'a' is from Set A and 'b' is from Set B. Relations can take various forms; they may not need to adhere to strict rules and can include multiple pairs that connect the elements of the two sets.

While a function is a specific type of relation that associates each element in the first set with exactly one element in the second set, the term "relation" is more general and encompasses all types of pairings. Mapping is often used synonymously with functions and describes a similar concept. A sequence usually refers to an ordered list of numbers or objects where specific patterns are established, rather than a set of pairs linking two distinct sets. Thus, the most appropriate term for the broad scenario described in the question is relation.