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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.
In computing, the attribute domain is the set of values allowed in an attribute. [1] For example: Rooms in hotel (1–300) Age (1–99) Married (yes or no) Nationality (Nepalese, Indian, American, or British) Colors (Red, Yellow, Green) For the relational model it is a requirement that each part of a tuple be atomic. [2] The consequence is that ...
(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 ...
Each attribute can be a class or an individual. The kind of object and the kind of attribute determine the kind of relation between them. A relation between an object and an attribute express a fact that is specific to the object to which it is related. For example, the Ford Explorer object has attributes such as: has as name Ford Explorer
The above properties and operations that are marked "[d]" and "[e]", respectively, generalize to heterogeneous relations. An example of a heterogeneous relation is "ocean x borders continent y". The best-known examples are functions [f] with distinct domains and ranges, such as sqrt : N → R +.