TITLE: Mathematical definition of a relational database
QUESTION [6 upvotes]: I'm reading a very verbose textbook on database design, but I suspect that much of the book could be condensed into a few pages if the authors were not trying to avoid mathematical language. 
What is the mathematical definition of a relational database? Stated in a way that a pure mathematician would be satisfied with.

REPLY [2 votes]: To add to the earlier answer, from the preface of the book The relational model for database management: version 2 by Codd:

The relational model is solidly based on two parts of mathematics: first-order predicate logic and the theory of relations.

For more on first-order predicate logic and the theory of relations, I refer you to the following links:

First-order predicate logic

and

Theory of relations

Edit:  Let me try, as per the OP's request, to define a relational database in a few sentences.

A relational database is a collection of tables, which mathematically are called relations.  Each table consists of columns and rows, which are represented in tabular format as follows:

Say your relation is $R = \{(0,0), (0,1),(1,2),(1,3),(2,3),(3,4)\}$.  In tabular format, you can have it as: