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[Relation]
1. A relation is a subset of the set of ordered
tuples (A1, A2, ... Am) formed by the Cartesian
cross-product of sets S1 x ... x Sm where each
An is an element of Sn.
I might say, instead, because I think they logically go closely together, and again just as a suggestion, nothing more:
Relation - mathematically by a language of sets, a relation is an (ordered) array/tuple of elements drawn one each from a set of domains, in order, with duplicate domains allowed. This set of n-tuples, said to have degree, n, or to be 'n-ary', where the number of n-tuples is said to be its, cardinality. The relation is uniquely named with regard to other relations. It can both be imagined and represented as a 2-D grid, or table.
Tuple - also termed an, element, of a relation, it is an unordered set of n-attributes, each attribute drawn from a particular dimension or domain, as irreducible 'atomic' scalars or strings (though multiples, if a multi-valued domain, were once considered), and identified by unique name in order to a) express any relationship among any set of attributes and b) to allow the tuple to have no particular order. As an unordered tuple does not properly correspond with a set relation, the relation might be termed, instead, a relationship, which might more properly correspond with a table. The tuple can be imagined as a vector/array. The tuple can be imagined and represented as a rows in the table, its attributes as columns.
Primary key - a unique attribute or combination of attributes in each element which uniquely identify the element in a relationship.
Foreign key - in a one-to-one unique match, an attribute or combination of attributes in each element which uniquely matches the primary key in the element of another relationship. Received on Sat Feb 25 2006 - 05:42:18 CST