Cartesian product

From Online Dictionary of Crystallography

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<font color="blue">Produit cartésien</font> (''Fr''). <font color="red">Kartesisches Produkt</font> (''Ge''). <font color="green">Producto cartesiano</font> (''Sp''). <font color="brown">Прямое произведение множеств</font> (''Ru''). <font color="black">Prodotto cartesiano</font> (''It''). <font color="purple">直積集合</font> (''Ja'').  
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<font color="orange">جداء ديكارتي</font> (''Ar''); <font color="blue">Produit cartésien</font> (''Fr''); <font color="red">Kartesisches Produkt</font> (''Ge''); <font color="black">Prodotto cartesiano</font> (''It''); <font color="purple">直積集合</font> (''Ja''); <font color="brown">Прямое произведение множеств</font> (''Ru''); <font color="green">Producto cartesiano</font> (''Sp'').

Revision as of 10:12, 12 October 2017

جداء ديكارتي (Ar); Produit cartésien (Fr); Kartesisches Produkt (Ge); Prodotto cartesiano (It); 直積集合 (Ja); Прямое произведение множеств (Ru); Producto cartesiano (Sp).


The Cartesian product is a direct product of sets.

The Cartesian product of two sets X and Y, denoted X × Y, is the set of all possible ordered pairs whose first component is a member of X and whose second component is a member of Y:

X\times Y = \{(x,y) | x\in X\;\mathrm{and}\;y\in Y\}.

A Cartesian product of two finite sets can be represented by a table, with one set as the rows and the other as the columns, and forming the ordered pairs, the cells of the table, by choosing the element of the set from the row and the column.