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In database theory, a relation, as originally defined by E. F. Codd, [1] is a set of tuples (d 1,d 2,...,d n), where each element d j is a member of D j, a data domain. Codd's original definition notwithstanding, and contrary to the usual definition in mathematics, there is no ordering to the elements of the tuples of a relation.
Thus, the "relation" in "relational database" refers to the various tables in the database; a relation is a set of tuples. The columns enumerate the various attributes of the entity (the employee's name, address or phone number, for example), and a row is an actual instance of the entity (a specific employee) that is represented by the relation.
The relational algebra uses set union, set difference, and Cartesian product from set theory, and adds additional constraints to these operators to create new ones.. For set union and set difference, the two relations involved must be union-compatible—that is, the two relations must have the same set of attributes.
The next definition defines relation that formalizes the contents of a table as it is defined in the relational model. Relation A relation is a tuple (,) with , the header, and , the body, a set of tuples that all have the domain .
In relational databases, relvar is a term introduced by C. J. Date and Hugh Darwen as an abbreviation for relation variable in their 1995 paper The Third Manifesto, to avoid the confusion sometimes arising from the use of the term "relation", by the inventor of the relational model, E. F. Codd, for a variable to which a relation is assigned as well as for the relation itself.
A relation is in first normal form if and only if no attribute domain has relations as elements. [1] Or more informally, that no table column can have tables as values. Database normalization is the process of representing a database in terms of relations in standard normal forms, where first normal is a minimal requirement.
An object–relational database (ORD), or object–relational database management system (ORDBMS), is a database management system (DBMS) similar to a relational database, but with an object-oriented database model: objects, classes and inheritance are directly supported in database schemas and in the query language.
Every relation without NULL values will have at least one candidate key: Since there cannot be duplicate rows, the set of all columns is a superkey, and if that is not minimal, some subset of that will be minimal. There is a functional dependency from the candidate key to all the attributes in the relation.