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The Nested Set model is appropriate where the tree element and one or two attributes are the only data, but is a poor choice when more complex relational data exists for the elements in the tree. Given an arbitrary starting depth for a category of 'Vehicles' and a child of 'Cars' with a child of 'Mercedes', a foreign key table relationship must ...
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.
Set operations in SQL is a type of operations which allow the results of multiple queries to be combined into a single result set. [ 1 ] Set operators in SQL include UNION , INTERSECT , and EXCEPT , which mathematically correspond to the concepts of union , intersection and set difference .
Customarily X is called the determinant set and Y the dependent set. A functional dependency FD: X → Y is called trivial if Y is a subset of X. In other words, a dependency FD: X → Y means that the values of Y are determined by the values of X. Two tuples sharing the same values of X will necessarily have the same values of Y.
Note that self-decomposable aggregation functions can be combined (formally, taking the product) by applying them separately, so for instance one can compute both the SUM and COUNT at the same time, by tracking two numbers. More generally, one can define a decomposable aggregation function f as one that can be expressed as the composition of a ...
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
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 mathematical sense of a finitary relation , a set of tuples on some set of n sets S 1 , S 2 ,...., S n . [ 4 ]
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 ...