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Codd's theorem states that relational algebra and the domain-independent relational calculus queries, two well-known foundational query languages for the relational model, are precisely equivalent in expressive power. That is, a database query can be formulated in one language if and only if it can be expressed in the other.
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.
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.
An alternate representation of the previous example would be: { , ,, , ′ ′, } In this example, the value of the requested F domain is directly placed in the formula and the C domain variable is re-used in the query for the existence of a department, since it already holds a crew member's ID.
For example, in the Order relation the attribute Customer ID is a foreign key. A join is the operation that draws on information from several relations at once. By joining relvars from the example above we could query the database for all of the Customers, Orders, and Invoices.
In relational algebra, a selection (sometimes called a restriction in reference to E.F. Codd's 1970 paper [1] and not, contrary to a popular belief, to avoid confusion with SQL's use of SELECT, since Codd's article predates the existence of SQL) is a unary operation that denotes a subset of a relation.
A relational database schema is defined as a tuple S = (D, R, h) where D is the domain of atomic values (see relational model for more on the notions of domain and atomic value), R is a finite set of relation names, and h : R → 2 C. a function that associates a header with each relation name in R. (Note that this is a simplification from the ...
The database schema is the structure of a database described in a formal language supported typically by a relational database management system (RDBMS). The term " schema " refers to the organization of data as a blueprint of how the database is constructed (divided into database tables in the case of relational databases ).