Algebra . Relational Algebra is : the formal description of how a relational database operates an interface to the data stored in the database itself the mathematics which underpin SQL operations Operators in relational algebra are not necessarily the same as SQL operators , even if they have the same name . For example , the SELECT statement exists in SQL , and also exists in relational algebra . These two uses of SELECT are not the same . The DBMS must take whatever SQL statements the user types in and translate them into relational algebra operations before applying them to the database . Terminology Relation - a set of tuples . Tuple - a collection of attributes which describe some real world entity . Attribute - a real world role played by a named domain . Domain - a set of atomic values . Set - a mathematical definition for a collection of objects which contains no duplicates . Operators - Write INSERT - provides a list of attribute values for a new tuple in a relation . This operator is the same as SQL . DELETE - provides a condition on the attributes of a relation to determine which tuple ( s ) to remove from the relation . This operator is the same as SQL . MODIFY - changes the values of one or more attributes in one or more tuples of a relation , as identified by a condition operating on the attributes of the relation . This is equivalent to SQL UPDATE . Operators - Retrieval There are two groups of operations : Mathematical set theory based relations : UNION , INTERSECTION , DIFFERENCE , and CARTESIAN