Cartesian product

All three can similarly be defined for the Cartesian product of more than two sets.

See also orders on the Cartesian product of totally ordered sets.

The composite or record type is a Cartesian product with labels for the fields.

Here is the construction: take the Cartesian product of a surface with the unit interval.

Even if each of the is nonempty, the Cartesian product may be empty in general.

Thus the superstructure will contain the various desired Cartesian products.

The rook's graph is the Cartesian product of two complete graphs.

We return Cartesian product of the n resulting intervals.

Then, the members of are exactly those of the Cartesian product .

Sequences are arbitrary Cartesian products of a combinatorial object with itself.

This definition relies on the notion of the cartesian product.

In contrast, the usual torus is the Cartesian product of two circles only.

The Cartesian product is not a product in the category of graphs.

It is a cartesian product as a set, but with a particular multiplication operation.

To make the correspondence clear, a type constructor for the Cartesian product is typically added to the above.

Thus, the cardinality of the Cartesian product of no sets is 1.

The empty Cartesian product of functions is again the empty function.

The Cartesian product of manifolds is also a manifold.

Compare this to the notation for the Cartesian product of a family of sets.

Note that this is different from the standard cartesian product of functions considered as sets.

One can even form the Cartesian product of a collection of infinitely many sets (see exercise 6.3.20).

As a set, is the cartesian product N x H.

The Cartesian product of two circles may be taken to obtain a duocylinder.

The cartesian product of two curves also provides examples.

Such definitions make it possible to speak about (disjoint) unions or Cartesian products of types.