Home

Relationen

Relationen, the plural of the German term for relation, denote the concept of connections or associations studied across disciplines. In mathematics and logic, a relation on a set A is a subset of the Cartesian product A^n; most commonly one considers binary relations, a subset of A×A, describing when two elements are in a given relation. If a and b are related by R, we write a R b. Examples include equality (a = b), order (a < b) on numbers, and divisibility (a | b). Relations can be analyzed by properties such as reflexivity (every a R a), symmetry (a R b implies b R a), and transitivity (a R b and b R c imply a R c). Antisymmetry, equivalence relations (reflexive, symmetric, transitive), and partial orders (reflexive, antisymmetric, transitive) are important special cases. A relation can also have a converse and a composition with other relations, and it may be represented as a directed graph with elements as vertices and related pairs as edges.

In computer science and information systems, a relation often refers to a database table in the relational

Beyond math and databases, relations are used in linguistics to describe semantic roles, in philosophy to discuss

model
introduced
by
E.
F.
Codd.
A
relation
consists
of
a
set
of
tuples,
each
matching
a
fixed
schema
of
attributes.
Operations
such
as
selection,
projection,
and
join
manipulate
relations,
and
keys
enforce
unique
identification
of
tuples
while
referential
integrity
links
related
tables.
relational
properties,
and
in
graph
theory
where
a
relation
corresponds
to
directed
edges.
A
function
is
a
special
kind
of
relation
with
a
unique
output
for
each
input.