An Entity of Type: EndProduct103287178, from Named Graph: http://dbpedia.org, within Data Space: dbpedia.org

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 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).

Property Value
dbo:abstract
• 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 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. (en)
dbo:thumbnail
dbo:wikiPageID
• 24104095 (xsd:integer)
dbo:wikiPageLength
• 20274 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID
• 1124218294 (xsd:integer)
dbp:align
• center (en)
dbp:caption
• = ∩ . (en)
• A × = \ (en)
• A × = ∩ , (en)
• A × = ∪ , and (en)
• Example sets (en)
• and = {x&thinsp;∈&thinsp;ℝ : 4&thinsp;≤&thinsp;x&thinsp;≤&thinsp;7}, demonstrating (en)
• &thinsp;=&thinsp;{x&thinsp;∈&thinsp;ℝ : 2&thinsp;≤&thinsp;x&thinsp;≤&thinsp;5}, &thinsp;=&thinsp;{x&thinsp;∈&thinsp;ℝ : 3&thinsp;≤&thinsp;x&thinsp;≤&thinsp;7}, (en)
• &thinsp;=&thinsp;{y&thinsp;∈&thinsp;ℝ :&thinsp;1&thinsp;≤&thinsp;y&thinsp;≤&thinsp;3}, &thinsp;=&thinsp;{y&thinsp;∈&thinsp;ℝ : 2&thinsp;≤&thinsp;y&thinsp;≤&thinsp;4}, demonstrating (en)
• ≠ ∪ can be seen from the same example. (en)
• &thinsp;=&thinsp;{y&thinsp;∈&thinsp;ℝ :&thinsp;1&thinsp;≤&thinsp;y&thinsp;≤&thinsp;4}, &thinsp;=&thinsp;{x&thinsp;∈&thinsp;ℝ : 2&thinsp;≤&thinsp;x&thinsp;≤&thinsp;5}, (en)
dbp:id
• p/d032730 (en)
dbp:image
• CartDistr_svg.svg (en)
• CartInts_svg.svg (en)
• CartUnion_svg.svg (en)
dbp:title
• Direct product (en)
dbp:totalWidth
• 750 (xsd:integer)
dbp:wikiPageUsesTemplate
dcterms:subject
rdf:type
rdfs:comment
• 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 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). (en)
rdfs:label
• Cartesian product (en)
rdfs:seeAlso
owl:sameAs
prov:wasDerivedFrom
foaf:depiction
foaf:isPrimaryTopicOf
is dbo:wikiPageDisambiguates of
is dbo:wikiPageRedirects of