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.

See also tuple.
References in periodicals archive ?
Now we give the definition of the Cartesian product of neutrosophic soft sets.
From now on, we always use this version of the cartesian product with a derivative of one of the [H.sub.i]'s.
Then, a cartesian product on [[psi].sub.K] is obtained as follows.
Then their cartesian product is ([[GAMMA].sub.Q], A) x ([[PSI].sub.Q], B) = ([[ohm].sub.Q], A x B) where [[ohm].sub.Q](a, b) = [[GAMMA].sub.Q](a) x [[PSI].sub.Q](b) for (a, b) E A x B.
From the definition of Cartesian product graphs, for every vertex ([q.sub.1], [q.sub.2]) [member of] [V.sub.1] x [V.sub.2], we have
More generally, graphs with multiple arcs joining a pair of vertices can be defined, and the Cartesian product definition above can be applied in this case as well.
The domination related questions on the Cartesian product seems to be the most problematic among the standard products.
If [G.sub.1] and [G.sub.2] are the strong interval valued neutrosophic graphs, then the cartesian product [G.sub.1] x [G.sub.2]is a strong interval valued neutrosophic graph.
If [PI] is an equitable partition in any graph [GAMMA] and [DELTA] is an equitable partition in another graph [SIGMA], then {P x P' | P [member of] [PI], P' [member of] [DELTA]} is an equitable partition in the cartesian product graph [GAMMA] x [SIGMA].
Let [[??].sup.n.sub.i=1] [G.sub.i] be Cartesian product of n [greater than or equal to] 2 connected graphs [G.sub.i].
We first give the definition of cartesian product of fuzzy SU-ideals and cartesian product of anti fuzzy SU-ideals on SU-algebra and provide some its properties.
The diwebgraph (m, n) denoted shortly by [??](m, n) is the digraph obtained by taking the Cartesian product of [C.sub.m] and [P.sub.n].