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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 body is a set of tuples. A tuple is a collection of n values, where n is the relation's degree, and each value in the tuple corresponds to a unique attribute. [6] The number of tuples in this set is the relation's cardinality. [7]: 17–22 Relations are represented by relational variables or relvars, which can be reassigned.
(t.name = "Codd") — tuple t has a name attribute and its value is "Codd" Book(t) — tuple t is present in relation Book. The formal semantics of such atoms is defined given a database db over S and a tuple variable binding val : V → T D that maps tuple variables to tuples over the domain in S: v.a = w.b is true if and only if val(v)(a ...
That is, the Cartesian product of a set of n-tuples with a set of m-tuples yields a set of "flattened" (n + m)-tuples (whereas basic set theory would have prescribed a set of 2-tuples, each containing an n-tuple and an m-tuple). More formally, R × S is defined as follows:
The relational calculus consists of two calculi, the tuple relational calculus and the domain relational calculus, that is part of the relational model for databases and provide a declarative way to specify database queries.
In a relational database, a row or "record" or "tuple", represents a single, implicitly structured data item in a table. A database table can be thought of as consisting of rows and columns. [1] Each row in a table represents a set of related data, and every row in the table has the same structure.
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.
An n-tuple is a tuple of n elements, where n is a non-negative integer. There is only one 0-tuple, called the empty tuple. A 1-tuple and a 2-tuple are commonly called a singleton and an ordered pair, respectively. The term "infinite tuple" is occasionally used for "infinite sequences".