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IEVref:102-01-06ID:
Language:enStatus: Standard
Term: Cartesian product
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Definition: 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.


Publication date:2008-08
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Internal notes:2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO
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