# Cartesian product

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## cartesian product

[kär′tē·zhan ′präd·əkt]
(mathematics)
In reference to the product of P and Q, the set P × Q of all pairs (p,q), where p belongs to P and q belongs to Q.

## Cartesian product

(mathematics)
(After Renee Descartes, French philosper and mathematician) The Cartesian product of two sets A and B is the set

A x B = a, b) | a in A, b in .

I.e. the product set contains all possible combinations of one element from each set. The idea can be extended to products of any number of sets.

If we consider the elements in sets A and B as points along perpendicular axes in a two-dimensional space then the elements of the product are the "Cartesian coordinates" of points in that space.

References in periodicals archive ?
The aim of this paper is to show how the problem of finding efficient open domination graphs among Cartesian products can be approached by partitioning the vertex set of one factor.
We now recall the cartesian product of two graphs [GAMMA] and [SIGMA].
In textual form, R is in this case a proper subset of the Cartesian product of X and Y.
Moreover, Cartesian products, projections, selections, unions, and differences of induced subobjects satisfy all the abstract properties that are axiomatized by relational calculus (15; 16).
Another possible extension is to functions bandlimited to the Cartesian product of two (or more) balls.
In this section, we define the theoretical annotated temporal algebra and provide definitions for compaction, intersection, union, selection, difference, cartesian product, projection, and join on annotated relations.
Next, in Section 3, we refine it for the case when the partial ordering is a Cartesian product of component partial orderings, and in Section 4 explain how the introduced notions should be related to the constraint satisfaction problems.
In the next section, we introduce higraphs, first modifying Euler/Venn diagrams somewhat, then extending them to represent the Cartesian product, and finally connecting the resulting curves by edges or hyperedges.
This is done by maximizing the number of cartesian products and joins with two operators as children.
vt] operators (and their transaction time and bitemporal variants), as well as by ensuring that the timestamps are retained in the temporal Cartesian product operator.
The most studied graph products are the Cartesian product, the strong product, the direct product and the lexicographic product which are also called standard products.
The only difference with the pointing operation considered in [6] is at the end of the recursion, where instead of a new terminal of size 0, the pointing operation is equal to the cartesian product of [y.

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