This identity is often modeled as an "ordered triple" of an entity, property type, and time).

With the definition of a function as an ordered triple this would always be considered a partial function.

A model is thus an ordered triple, .

The data of the table are equivalent to the following set of ordered triples:

The signature of M is by definition the signature of Q, an ordered triple according to its definition.

This system can also be used for three-dimensional geometry, where every point in Euclidean space is represented by an ordered triple of coordinates (x, y, z).

In low-dimensional topology, the trigenus of a closed 3-manifold is an invariant consisting of an ordered triple .

He suggests that is replaced by , "with an ordered triple replacing the two ordered pairs and then being mappable to a ternary-branching tree" (pp. 17).

Let ρ be a binary operation on a set A. For each ordered triple of elements A we can evaluate their product in that order either as or.

In projective geometry, the harmonic conjugate point of an ordered triple of points on the real projective line is defined by the following construction:

This definition may be extended to a set A x B x C of ordered triples, and more generally to sets of ordered n-tuples for any positive integer n.

No matter what notation is employed, when the homogeneous coordinates of the point and line are just considered as ordered triples, their incidence is expressed as having their dot product equal 0.

The binary relation R itself is usually identified with its graph G, but some authors define it as an ordered triple (X, Y, G), which is otherwise referred to as a correspondence.

In general mathematics, a correspondence is an ordered triple (X,Y,R), where R is a relation from X to Y, i.e. any subset of the Cartesian product XxY.

In practice, this is not a problem because if this disjointness does not hold, it can be assured by appending the domain and codomain to the morphisms, (say, as the second and third components of an ordered triple).

Similarly, a binary truth function maps ordered pairs of truth values onto truth values, while a ternary truth function maps ordered triples of truth values onto truth values, and so on.

B6 and B7 enable what Converses and Association enable: given any class X of ordered triples, there exists another class Y whose members are the members of X each reordered in the same way.

(A minor modification needs to be made to the concept of the ordered triple (X, Y, G), as normally a proper class cannot be a member of an ordered tuple; or of course one can identify the function with its graph in this context.)

Firstly, the projective linear group PGL(2,K) is sharply 3-transitive - for any two ordered triples of distinct points, there is a unique map that takes one triple to the other, just as for Möbius transforms, and by the same algebraic proof (essentially dimension counting, as the group is 3-dimensional).