SQL and Relational Theory, 2nd Edition

WHAT’S A RELATION?

I’ll use our usual suppliers relation as a basis for examples in this section. Here’s a picture:

SNO | CHAR	SNAME | CHAR	STATUS | INTEGER	CITY | CHAR
S1	Smith	20	London
S2	Jones	10	Paris
S3	Blake	30	Paris
S4	Clark	20	London
S5	Adams	30	Athens

And here’s a definition:

Definition: Let {H} be a tuple heading and let t1, t2, ..., tm (m ≥ 0) be distinct tuples, all with heading {H}.^[41] Then the combination, r say, of {H} and the set of tuples {t1, t2, ..., tm} is a relation value (or just a relation for short) over the attributes A1, A2, ..., An, where A1, A2, ..., An are all of the attributes in {H}. The heading of r is {H}; r has the same attributes (and hence the same attribute names and types) and the same degree as that heading does. The set of tuples {t1, t2, ..., tm} is the body of r. The value m is the cardinality of r.

I’ll leave it as an exercise for you to interpret the suppliers relation in terms of the foregoing definition. However, I will at least explain why we call such things relations. Basically, each tuple in a relation represents an n-ary relationship, in the ordinary natural language sense of that term, interrelating a set of n values (one such value for each tuple attribute); the full set of tuples in a given relation represents the full set of such relationships that happen to exist at some given time; and, mathematically speaking, that set of tuples is a relation. Thus, the explanation often heard, to the effect that the relational model is so called because it lets ...