Database in Depth: Relational Theory for Practitioners

In this chapter I've presented precise definitions for the fundamental concepts tuple and relation. As I said in the introductory section, those definitions can be a little daunting at first, but I hope you were able to make sense of them after having read the first two chapters. I also discussed tuple and relation types, and showed some examples of tuple and relation selector invocations. And I discussed certain important consequences of the definitions:

• No tuple, and therefore no relation, ever contains any nulls.

• Every subset of a tuple is a tuple, every subset of a heading is a heading, and every subset of a body is a body (and those subsets can always be empty).

• Two tuples are equal if and only if they're the very same tuple.

Other consequences already covered in earlier chapters include:

• Every tuple contains exactly one value for each of its attributes, and relations are therefore always in first normal form.

• The attributes of a tuple, and therefore of a relation, are unordered, left to right.

• The tuples of a relation are also unordered, top to bottom.

• Relations never contain any duplicate tuples.

I also gave some important pragmatic arguments in favor of prohibiting both duplicates and nulls. And I finished up by briefly introducing the very important degree-zero relations TABLE_DUM and TABLE_DEE; DUM means NO or FALSE, and DEE means YES or TRUE.