Given a binary relation it is then possible to put all the elements of the set in a certain order.

The formal approach requires that we start with a study of binary relations.

The first approach is to treat equality as no different than any other binary relation.

In the semantic web, a property is a binary relation.

Binary relations are also heavily used in computer science.

That is, they are the binary relations describing how subsets meet.

Some important types of binary relations over a set X are:

Strict weak ordering is a binary relation on a set.

The second is the level of binary relations or relational mappings.

In set theory, the transitive closure of a binary relation.

Higher order relations are converted into collections of binary relations.

This is closely related to the notion of reflexivity for binary relations.

On any given set few (if any!) binary relations will have mathematical significance.

A relation with two attributes is known as a binary relation.

Thus the binary relation is functional in each direction: can also act as a key to .

A property is a directed binary relation that specifies class characteristics.

The concept of function is defined as a special kind of binary relation.

The ordinary signature for set theory includes a single binary relation .

This definition agrees with the definition of union for binary relations.

A ternary relation however is always expressable as two binary relations.

This properties on binary relations can be easily checked by definition:

Such a matrix can be used to represent a binary relation between a pair of finite sets.

In the special case with just one binary relation, we obtain the notion of a graph homomorphism.

The principle is quite simple (here for single binary Relations and without constants):

This contrasts with a general binary relation, which can be viewed as being a multi-valued function.