What is cartesian product?

Cartesian Product

In mathematics, a Cartesian product (or product set) is a construction to build a new set out of a number of given sets. Each member of the Cartesian product corresponds to the selection of one element each in every one of those sets. The Cartesian product is named after René Descartes, whose formulation of analytic geometry gave rise to the concept.

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Some articles on cartesian product:

Cartesian Product - Graph Theory
... In graph theory the Cartesian product of two graphs G and H is the graph denoted by G×H whose vertex set is the (ordinary) Cartesian product V(G)×V(H) and ... The Cartesian product of graphs is not a product in the sense of category theory ... Instead, the categorical product is known as the tensor product of graphs ...
Predicate Functor Logic - Kuhn's Formalization - Axioms and Semantics
... Cartesian product, Here only, Quine adopted an infix notation, because this infix notation for Cartesian product is very well established in mathematics ... Cartesian product allows restating conjunction as follows Reorder the concatenated argument list so as to shift a pair of duplicate variables to the far left, then invoke S to eliminate the ...
Reduced Product
... logic, and in algebra, the reduced product is a construction that generalizes both direct product and ultraproduct ... The domain of the reduced product is the quotient of the Cartesian product by a certain equivalence relation ~ two elements (ai) and (bi) of the Cartesian product are ... If U is an ultrafilter, the reduced product is an ultraproduct ...
Vienna Development Method - VDM Features - Type Constructors: Union, Product and Composite Types
... Tn Union of types T1...Tn T1*T2*...*Tn Cartesian product of types T1...Tn T f1T1.. ... Cartesian product types may also be defined in VDM-SL ... The composite or record type is a Cartesian product with labels for the fields ...
Colexicographical Order
... In mathematics, the colexicographic or colex order, is a natural order structure of the Cartesian product of two or more ordered sets ... Given two partially ordered sets A and B, the colexicographical order on the Cartesian product A × B is defined as (a,b) ≤ (a′,b′) if and only if b < b′ or (b = b′ and a ≤ a ... define the colexicographic order on the Cartesian product of n ordered sets ...

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