What does Cartesian product mean?
Definitions for Cartesian product
carte·sian prod·uct
This dictionary definitions page includes all the possible meanings, example usage and translations of the word Cartesian product.
Princeton's WordNet
intersection, product, Cartesian productnoun
the set of elements common to two or more sets
"the set of red hats is the intersection of the set of hats and the set of red things"
Wiktionary
Cartesian productnoun
The set of all possible pairs of elements whose components are members of two sets. Notation: .
Wikipedia
Cartesian product
In mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is in A and b is in B. In terms of set-builder notation, that is A × B = { ( a , b ) ∣ a ∈ A and b ∈ B } . {\displaystyle A\times B=\{(a,b)\mid a\in A\ {\mbox{ and }}\ b\in B\}.} A table can be created by taking the Cartesian product of a set of rows and a set of columns. If the Cartesian product rows × columns is taken, the cells of the table contain ordered pairs of the form (row value, column value).One can similarly define the Cartesian product of n sets, also known as an n-fold Cartesian product, which can be represented by an n-dimensional array, where each element is an n-tuple. An ordered pair is a 2-tuple or couple. More generally still, one can define the Cartesian product of an indexed family of sets. The Cartesian product is named after René Descartes, whose formulation of analytic geometry gave rise to the concept, which is further generalized in terms of direct product.
Wikidata
Cartesian product
In mathematics, a Cartesian product is a mathematical operation which returns a set from multiple sets. That is, for sets A and B, the Cartesian product A × B is the set of all ordered pairs where a ∈ A and b ∈ B. The simplest case of a Cartesian product is the Cartesian square, which returns a set from two sets. A table can be created by taking the Cartesian product of a set of rows and a set of columns. If the Cartesian product rows × columns is taken, the cells of the table contain ordered pairs of the form. If the Cartesian product is columns × rows is taken, the cells of the table contain the ordered pairs of the form. A Cartesian product of n sets can be represented by an array of n dimensions, where each element is an n-tuple. An ordered pair is a 2-tuple. The Cartesian product is named after René Descartes, whose formulation of analytic geometry gave rise to the concept.
Suggested Resources
cartesian product
The cartesian product symbol -- In this Symbols.com article you will learn about the meaning of the cartesian product symbol and its characteristic.
Matched Categories
Numerology
Chaldean Numerology
The numerical value of Cartesian product in Chaldean Numerology is: 5
Pythagorean Numerology
The numerical value of Cartesian product in Pythagorean Numerology is: 7
Translations for Cartesian product
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"Cartesian product." Definitions.net. STANDS4 LLC, 2024. Web. 4 May 2024. <https://www.definitions.net/definition/Cartesian+product>.
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