Cartesian product

Etymology
From +, after French philosopher, mathematician, and scientist  (1596–1650), whose formulation of analytic geometry gave rise to the concept.

Noun

 * 1)  The set of all possible ordered pairs of elements, the being first from $$X$$, the second from $$Y$$, written $$X \times Y$$. Formally, the set $$\{(x,y)\; |\; x\in X \; \text{and} \; y\in Y\}$$.
 * 2)  All possible combinations of rows between all of the tables listed.
 * 3)  An (m+n)-dimensional space, formally composed of all possible ordered pairs of points from $$X$$ and $$Y$$, but thought of as an independent (m+n)-dimensional space (in the sense that if, e.g. $$X$$ and $$Y$$ are vector spaces, the elements of $$X \times Y$$ are thought of as (m+n)-tuples instead of ordered pairs) and written $$ X \times Y$$.

Translations

 * Chinese:
 * Mandarin: 笛卡兒積, 笛卡爾乘積
 * Czech: kartézský součin
 * Dutch: cartesisch product, kruisproduct
 * Estonian: Cartesiuse korrutis, otsekorrutis, ristikorrutis
 * Finnish: karteesinen tulo, tulojoukko
 * French:
 * German: kartesisches Produkt,
 * Greek:
 * Italian: prodotto cartesiano
 * Japanese: デカルト積,
 * Polish: iloczyn kartezjański, produkt kartezjański
 * Portuguese: produto cartesiano
 * Romanian: produs cartezian
 * Russian: дека́ртово произведе́ние, прямо́е произведе́ние
 * Serbo-Croatian: Kartezijev produkt
 * Spanish: producto cartesiano