Understanding the Difference Between Relation and Table in a Relational Database

The terms 'relation' and 'table' are fundamental concepts in the realm of relational databases. Yet, many find the differences between the two to be somewhat puzzling. This article aims to clarify these concepts, drawing on the practical example of a bookkeeping system and theoretical foundations of set theory.

A Practical Example: Old-Fashioned Bookkeeping vs. Modern Computerized System

Imagine a company based on an 'old-fashioned' bookeeping system, where each customer's information is manually stored in binders. Each binder contains a copy of every customer's invoice. For easy retrieval, these binders are organized in an alphabetical rollodex. This system, although functional, is inefficient and prone to errors.

Once the company switches to a computerized bookkeeping system, the rollodex becomes an electronic customers table, and the binders become an electronic invoices table. In both cases, the customer number serves as the key to link the two: the customers table (rollodex) and the invoices table (binders). In both systems, the customer number acts as a relation, linking the two sets of data.

The relational database takes this concept to a new level, where the database query searches for a customer's record and uses the customer's number to retrieve all or part of their invoices. This is a direct application of the concept of 'relation', which we will explore in more detail below.

Theoretical Foundations: SET Theory and Relational Algebra

To truly understand the concepts of 'relation' and 'table', one must study the theoretical foundations of set theory. This is crucial because relational database technology is fundamentally based on set theory, a branch of mathematics that deals with collections of objects.Each record in a relational database can be thought of as a set of attributes, and a table is a collection of such records, forming a larger set.

Dr. E.F. Codd, who is considered the father of relational databases, laid out the principles of relational database management systems (RDBMS) in his seminal paper, A Relational Model of Data for Large Shared Data Banks. Understanding Dr. Codd's work is essential to grasping the nuances of relational databases, relations, and tables.

Defining 'Table' and 'Relation'

Table

When we talk about a 'table' in the context of a relational database, we are referring to a structured collection of data stored in a database. Each table is composed of rows (records) and columns (fields). A table can be visualized as a spreadsheet with a fixed schema. For example, in a customers table, each row represents a different customer, and each column represents a specific attribute like the customer's name, address, or invoice number.

Relation

A 'relation' is a term from relational algebra and is a more abstract concept. It can be understood as a set of tuples (rows) and their corresponding attributes (columns). A relation does not have the inherent structure of a table; it is a mathematical construct representing a set of values.

In simpler terms, a relation is a logical set of data, while a table is a structured, physical representation of that data. A table can be considered a relation, but a relation can also span multiple tables. For example, a customer table and an invoice table can both be relations, and they can be joined to form a more complex relation that represents a complete record of customer interactions.

Key Concepts: One-to-Many Relationships

One of the most common types of relationships in relational databases is the one-to-many relationship. In our example, a customer can have many invoices, which is represented as a one-to-many relationship between the customers table and the invoices table. This relationship is maintained through a common attribute, usually a customer number, that links the two tables.

In SQL, you can use joins and subqueries to represent complex relations. For instance, a SQL join can merge records from two tables based on a related column, effectively forming a relation that combines the data from both tables. Similarly, subqueries can be used to retrieve data from one table based on conditions defined in another table, further elaborating on the concept of relations.

Conclusion

The concepts of 'table' and 'relation' are crucial in understanding relational databases. While a table provides a structured, physical representation of data, a relation is a more abstract, logical set of data. Both terms are interconnected and often used interchangeably, but it is important to understand their nuances.

By studying set theory and delving into the work of pioneers like Dr. E.F. Codd, one can gain a deeper understanding of how these concepts function in the real world. The more familiar you are with these foundational principles, the better you will be at designing, querying, and managing relational databases.