Cartesian product of several sets

URNurn:iso:std:iso:80000:-2:ed-2:en:item:2-6.17

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https://metanorma.github.io/isq-smart/math/part-2-6/t2-6.17
urn:iso:std:iso:80000:-2:ed-2:en:item:2-6.17

ISQ Identifiers

ISO

urn:iso:std:iso:80000:-2:ed-2:en:item:2-6.17

IEC

urn:iec:std:iec:80000-2:2019:::item:2-6.17

Designations

ENCartesian product of several sets

FRproduit cartésien de plusieurs ensembles

Symbol

\prod_{i = 1}^{n} A_{i}

Notation systems

AsciiMath

prod_(i=1)^n A_i

LaTeX

\prod_{i = 1}^{n} A_{i}

Definition

Cartesian product of the sets +

$A_{1}, A_{2}, \dots, A_{n}$ +

$\prod_{i = 1}^{n} A_{i} = A_{1} \times \dots \times A_{n}$

produit cartésien des ensembles +

$A_{1}, A_{2}, \dots, A_{n}$ +

$\prod_{i = 1}^{n} A_{i} = A_{1} \times \dots \times A_{n}$

Notes

The set of ordered $n$ -tuples $(x_{1}, x_{2}, \dots, x_{n})$ such that $x_{1} \in A_{1}, x_{2} \in A_{2}, \dots, x_{n} \in A_{n}$ .

$A \times A \times \dots \times A$ is denoted by $A^{n}$ , where $n$ is the number of factors in the product.

Ensembles des $n$ -uples $(x_{1}, x_{2}, \dots, x_{n})$ pour lesquels $x_{1} \in A_{1}, x_{2} \in A_{2}, \dots, x_{n} \in A_{n}$ .

$A \times A \times \dots \times A$ est noté $A^{n}$ , où $n$ est le nombre de facteurs dans le produit.

Referenced by

multiplication

Ontology
isq:MathConcept smart:TermEntry

Class Hierarchy

smart:Entity smart:TermEntryisq:MathConcept

A mathematical concept as defined in ISO/IEC 80000 Part 2.

Instance IRI

isq:t2-6.17

Properties

isq:MathConceptShape

Property	Value
rdf:type	isq:MathConcept smart:TermEntry
dcterms:identifier	2-6.17
skosxl:prefLabel	"Cartesian product of several sets"@en
skosxl:altLabel	"prod_(i=1)^n A_i"@en
skos:definition	Cartesian product of the sets + stem:[A_1, A_2, ..., A_n] + stem:[prod_(i=1)^n A_i = A_1 xx ... xx A_n]
skos:note	The set of ordered stem:[n]-tuples stem:[(x_1, x_2, ..., x_n)] such that stem:[x_1 in A_1, x_2 in A_2, ..., x_n in A_n].…
smart:hasBindingnessType	bindingness-type:normative
dcterms:isPartOf	isq:part-2-6

Related Entities

isq:MathConceptShape isq:part-2-6 smart:TermEntry