binary relation
التعريفات والمعاني
== English ==
=== Pronunciation ===
(General American) IPA(key): /ˈbaɪ.ner.i rɪˈleɪ.ʃən/
=== Noun ===
binary relation (plural binary relations)
(set theory, order theory, "on" a set A) A subset of the Cartesian product
A
×
A
{\displaystyle A\times A}
(the set of ordered pairs (
a
{\displaystyle a}
,
b
{\displaystyle b}
) of elements of
A
{\displaystyle A}
, alternatively written as
A
2
{\displaystyle A^{2}}
).
Synonym: homogeneous relation
(set theory, order theory, "on" or "between" sets A and B) A subset of the Cartesian product
A
×
B
{\displaystyle A\times B}
.
Synonym: heterogeneous relation
==== Usage notes ====
If
R
{\displaystyle R}
is a relation between
A
{\displaystyle A}
and
B
{\displaystyle B}
, then
A
{\displaystyle A}
is called the domain of the relation, and
B
{\displaystyle B}
is called the codomain of the relation.
For a binary relation
R
{\displaystyle R}
, the notation
a
R
b
{\displaystyle aRb}
signifies that
(
a
,
b
)
∈
R
{\displaystyle (a,b)\in R}
, and one may say that
a
{\displaystyle a}
is in binary relation
R
{\displaystyle R}
to
b
{\displaystyle b}
.
==== Synonyms ====
(order theory): correspondence, dyadic relation, 2-place relation
==== Hyponyms ====
(order theory): dependency relation, equivalence relation
==== Translations ====
=== See also ===
nil relation (the empty set)
universal relation (the entire set A×A)
=== Further reading ===
Finitary relation on Wikipedia.Wikipedia
Order theory on Wikipedia.Wikipedia
Binary relation on Encyclopedia of Mathematics
Binary Relation on Wolfram MathWorld