On making relational division comprehensible

Division is the most intellectually challenging of the basic operators of relational algebra. Although its utility is unquestioned, its presentation by many textbooks, and therefore by many instructors, leaves much to be desired. This paper examines the standard approaches used to express division in relational algebra and SQL, explains the derivation of each, and presents a coherent sequence of examples that we have used successfully to teach division to students in introductory database classes.