In mathematics and logic, "first-order" refers to a type of formal system that deals with objects and their relationships without quantifying over sets or higher-level structures. First-order logic allows for the use of predicates and quantifiers like "for all" and "there exists," enabling the expression of statements about individual elements within a domain. In computer science, "first-order" can describe functions or programming languages that do not allow for higher-order functions, which are functions that take other functions as arguments or return them as results. First-order programming focuses on basic operations and data types, making it simpler and more straightforward for certain applications.