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A relation is thus a heading paired with a body, the heading of the relation being also the heading of each tuple in its body. The number of attributes constituting a heading is called the degree, which term also applies to tuples and relations. The term n-tuple refers to a tuple of degree n (n ≥ 0). E. F. Codd used the term "relation" in its ...
However, unlike rows and columns in a table, a relation's attributes and tuples are unordered. A relation consists of a heading and a body. The heading defines a set of attributes, each with a name and data type (sometimes called a domain). The number of attributes in this set is the relation's degree or arity. The body is a set of tuples.
Constraints can apply to single attributes, to a tuple (restricting combinations of attributes) or to an entire relation. Since every attribute has an associated domain, there are constraints (domain constraints). The two principal rules for the relational model are known as entity integrity and referential integrity.
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 consequence is that each value in the tuple must be of some basic type, like a string or an integer. For the elementary type to be atomic it cannot be broken into more pieces. Alas, the domain is an elementary type, and attribute domain the domain a given attribute belongs to an abstraction belonging to or characteristic of an entity.
The named columns of the relation are called attributes, and the domain is the set of values the attributes are allowed to take. The basic data structure of the relational model is the table, where information about a particular entity (say, an employee) is represented in rows (also called tuples ) and columns.
(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 ...
Candidate key – minimal superkey for a relation. Foreign key – referential constraint between two tables. Primary key – Superkey – set of attributes of a relation variable for which it holds that in all relations assigned to that variable, there are no two distinct tuples (rows) that have the same values for the attributes in this set.