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Area Mathematics - General concepts and linear algebra / Sets and operations

IEV ref102-01-06

en
Cartesian product
for n given sets A 1 , A 2 ,, A n MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadgeadaWgaaWcba GaaeymaaqabaGccaqGSaGaaeiiaiaadgeadaWgaaWcbaGaaeOmaaqa baGccaGGSaGaeS47IWKaaiilaiaadgeadaWgaaWcbaGaamOBaaqaba aaaa@3F35@ , set, the elements of which are the ordered n-tuples ( a 1 , a 2 ,, a n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadggadaWgaaWcba GaaGymaaqabaGccaqGSaGaaeiiaiaadggadaWgaaWcbaGaaGOmaaqa baGccaGGSaGaeS47IWKaaiilaiaadggadaWgaaWcbaGaamOBaaqaba aaaa@4321@ ) of elements a 1 A 1 , a 2 A 2 ,, a n A n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadggadaWgaaWcba GaaGymaaqabaGccqGHiiIZcaWGbbWaaSbaaSqaaiaaigdaaeqaaOGa aeilaiaabccacaWGHbWaaSbaaSqaaiaaikdaaeqaaOGaeyicI4Saam yqamaaBaaaleaacaaIYaaabeaakiaacYcacqWIVlctcaGGSaGaamyy amaaBaaaleaacaWGUbaabeaakiabgIGiolaadgeadaWgaaWcbaGaam OBaaqabaaaaa@4D0B@

Note 1 to entry: The Cartesian product of sets A 1 , A 2 ,, A n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadgeadaWgaaWcba GaaGymaaqabaGccaqGSaGaaeiiaiaadgeadaWgaaWcbaGaaGOmaaqa baGccaGGSaGaeS47IWKaaiilaiaadgeadaWgaaWcbaGaamOBaaqaba aaaa@42C1@ is denoted by A 1 × A 2 ×× A n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadgeadaWgaaWcba GaaGymaaqabaGccqGHxdaTcaqGGaGaamyqamaaBaaaleaacaaIYaaa beaakiabgEna0kabl+UimjabgEna0kaadgeadaWgaaWcbaGaamOBaa qabaaaaa@46F7@ . The Cartesian product of the set A by itself n times is denoted by An.


fr
produit cartésien, m
pour n ensembles donnés A 1 , A 2 ,, A n MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadgeadaWgaaWcba GaaeymaaqabaGccaqGSaGaaeiiaiaadgeadaWgaaWcbaGaaeOmaaqa baGccaGGSaGaeS47IWKaaiilaiaadgeadaWgaaWcbaGaamOBaaqaba aaaa@3F35@ , ensemble dont les éléments sont les multiplets ordonnés ( a 1 , a 2 ,, a n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadggadaWgaaWcba GaaGymaaqabaGccaqGSaGaaeiiaiaadggadaWgaaWcbaGaaGOmaaqa baGccaGGSaGaeS47IWKaaiilaiaadggadaWgaaWcbaGaamOBaaqaba aaaa@4321@ ) d'éléments a 1 A 1 , a 2 A 2 ,, a n A n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadggadaWgaaWcba GaaGymaaqabaGccqGHiiIZcaWGbbWaaSbaaSqaaiaaigdaaeqaaOGa aeilaiaabccacaWGHbWaaSbaaSqaaiaaikdaaeqaaOGaeyicI4Saam yqamaaBaaaleaacaaIYaaabeaakiaacYcacqWIVlctcaGGSaGaamyy amaaBaaaleaacaWGUbaabeaakiabgIGiolaadgeadaWgaaWcbaGaam OBaaqabaaaaa@4D0B@

Note 1 à l'article: Le produit cartésien des ensembles A 1 , A 2 ,, A n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadgeadaWgaaWcba GaaGymaaqabaGccaqGSaGaaeiiaiaadgeadaWgaaWcbaGaaGOmaaqa baGccaGGSaGaeS47IWKaaiilaiaadgeadaWgaaWcbaGaamOBaaqaba aaaa@42C1@ est noté A 1 × A 2 ×× A n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadgeadaWgaaWcba GaaGymaaqabaGccqGHxdaTcaqGGaGaamyqamaaBaaaleaacaaIYaaa beaakiabgEna0kabl+UimjabgEna0kaadgeadaWgaaWcbaGaamOBaa qabaaaaa@46F7@ . Le produit cartésien de l'ensemble A par lui-même n fois est noté An.


de
kartesisches Produkt, n

es
producto cartesiano

ja
直積
カルテシアン積
デカルト積

pl
iloczyn kartezjański

pt
produto cartesiano

sr
Декартов производ, м јд

sv
kartesisk produkt

zh
笛卡儿积

Publication date: 2008-08
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