Reflexive Relation
In
logic
and
mathematics
, a
binary relation
R
over a set
X
is
reflexive
if for all
a
in
X
,
a
is related to itself. In
mathematical notation
, this is:
\forall a \in X,\ a R a
For example, "is greater than or equal to" is a reflexive relation but "is greater than" is not. Examples of reflexive relations include:
"is equal to" (
equality
)
"is a
subset
of" (set inclusion)
"is less than or equal to" and "is greater than or equal to" (
inequality
)
"divides" (
divisibility
)
A reflexive relation that is also
transitive
is a
preorder
. A preorder that is
antisymmetric
is a
partial order
. A preorder that is
symmetric
is an
equivalence relation
. The statement
\forall a \in X,\ a = a
is called the
axiom of equality
in some systems.
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