A relation in mathematics is a subset of the Cartesian product of two sets, R : A x B. If (a, b) is an element of R then we write a R b, meaning a is related to b by R. A relation may be: reflexive (a R a), symmetric (a R b => b R a), transitive (a R b & b R c => a R c), antisymmetric (a R b & b R a => a = b) or total (a R b or b R a).
There are several mathematical operations that can be done to a relation: select, project, union, difference, Cartesian product, and rename. See relational algebra.
A relational database stores data in relations called tables. Their data manipulation languages provide operations on tables that follow the relational algebra.
See equivalence relation, partial ordering, pre-order, total ordering.
Based on an entry from The Free On-line Dictionary of Computing, © 1993-2001 Denis Howe, used by permission.
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