Nullology

Nullology is the study of the empty set. Sets per se crop up all over the place in the relational world; the question is—and it’s a crucial one—what happens if the set under consideration happens to be empty? For example, a relation contains a set of tuples: What about the possibility of a relation containing no tuples at all? Now, this particular possibility is reasonably familiar, because a relation with no tuples behaves much like a file with no records. But even in this case, there are some interesting aspects to consider that are probably unfamiliar to most database professionals. And there are many other places in the relational world where the empty set rears its head, several of them both unfamiliar and of fundamental importance.

The presentation is divided into three modules. Module I covers the effect of “empty relations” (relations with no tuples) on the operators of the relational algebra. Module II introduces the (surprisingly important!) topic of relations with no attributes and shows their usefulness in a variety of a situations; it also discusses certain possibly unfamiliar aspects of the relational join operator. Module III considers the impact of nullological thinking on keys and functional dependencies.