Cartesian product

English

Alternative forms

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Etymology

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

Noun

1. Template:Lb 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. Template:Lb All possible combinations of rows between all of the tables listed.
3. Template:Lb 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 $X\times Y$.
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4. Template:Lb Template:Non-gloss
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Synonyms

• Template:Qualifier Template:L

Translations

• Chinese:

  Mandarin: Template:T, Template:T

• Czech: Template:T
• Dutch: Template:T, Template:T
• Estonian: Template:T, Template:T, Template:T
• Finnish: Template:T, Template:T
• French: Template:T+
• German: Template:T, Template:T+
• Greek: Template:T+
• Italian: Template:T
• Japanese: Template:T, Template:T+ Template:Qualifier
• Maori: Template:T
• Polish: Template:T, Template:T
• Portuguese: Template:T
• Romanian: Template:T
• Russian: Template:T, Template:T Template:Qualifier
• Serbo-Croatian: Template:T
• Spanish: Template:T