Combine related tuples from two different relations.
The Join operation, denoted by the symbol ⨝, is one of the most powerful and frequently used operations in relational algebra. It is a binary operation that allows us to combine related tuples from two different relations into a single new relation. The result contains all the attributes of both original relations. The most common type of join is the 'natural join'. A natural join R ⨝ S combines tuples from R and S that have the same values for all attributes that have the same name in both relations. The common attributes appear only once in the result. Another common type is the 'theta join' or 'conditional join'. It combines tuples based on a specified condition (the 'theta'). A special case of the theta join is the 'equijoin', where the condition only involves equality. For example, if we have an 'Employees' table with a 'dept_id' attribute and a 'Departments' table with a 'dept_id' attribute, we can join them on this common attribute. The result would be a new, wider relation containing employee information alongside the information for the department they belong to. The Join operation is fundamental for retrieving data that is spread across multiple tables, which is the standard practice in a normalized relational database. It corresponds to the various `JOIN` clauses (INNER JOIN, LEFT JOIN, etc.) in SQL.