Definitions for Cartesian product
carte·sian prod·uct

Princeton's WordNetRate this definition:0.0 / 0 votes

1. 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"

WiktionaryRate this definition:0.0 / 0 votes

1. Cartesian productnoun

   The set of all possible pairs of elements whose components are members of two sets. Notation: .

WikipediaRate this definition:0.0 / 0 votes

1. 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.

ChatGPTRate this definition:0.0 / 0 votes

1. cartesian product

   The Cartesian product, also known as a direct product, is a mathematical operation that returns a set from multiple sets. If we have two sets, say A and B, the Cartesian product is the set of all ordered pairs (a, b) where a is in A and b is in B. This concept is often extended to products of several sets, and is a fundamental concept in set theory and related areas of mathematics.

WikidataRate this definition:0.0 / 0 votes

1. 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.

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1. 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

1. • Set

How to pronounce Cartesian product?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say Cartesian product in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of Cartesian product in Chaldean Numerology is: 5

2. Pythagorean Numerology

   The numerical value of Cartesian product in Pythagorean Numerology is: 7

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=Cartesian product
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Cartesian_Product
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Cartesian_Product
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=Cartesian product