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Relation, tuple, and attribute represented as table, row, and column respectively. 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.
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.
In relational database theory, a functional dependency is the following constraint between two attribute sets in a relation: Given a relation R and attribute sets ,, X is said to functionally determine Y (written X → Y) if each X value is associated with precisely one Y value.
Difference is implemented in SQL in the form of the EXCEPT or MINUS operator. The cartesian product (X) of two relations is a join that is not restricted by any criteria, resulting in every tuple of the first relation being matched with every tuple of the second relation. The cartesian product is implemented in SQL as the Cross join operator.
A table in a SQL database schema corresponds to a predicate variable; the contents of a table to a relation; key constraints, other constraints, and SQL queries correspond to predicates. However, SQL databases deviate from the relational model in many details, and Codd fiercely argued against deviations that compromise the original principles. [3]
In a relational database, the schema defines the tables, fields, relationships, views, indexes, packages, procedures, functions, queues, triggers, types, sequences, materialized views, synonyms, database links, directories, XML schemas, and other elements. A database generally stores its schema in a data dictionary. Although a schema is defined ...
SQL was initially developed at IBM by Donald D. Chamberlin and Raymond F. Boyce after learning about the relational model from Edgar F. Codd [12] in the early 1970s. [13] This version, initially called SEQUEL (Structured English Query Language), was designed to manipulate and retrieve data stored in IBM's original quasirelational database management system, System R, which a group at IBM San ...
every element of Y \ X, the set difference between Y and X, is a prime attribute (i.e., each attribute in Y \ X is contained in some candidate key). To rephrase Zaniolo's definition more simply, the relation is in 3NF if and only if for every non-trivial functional dependency X → Y, X is a superkey or Y \ X consists of prime attributes.