English Dictionary

Cartesian product

noun

(set theory) The set of all possible pairs of elements whose components are members of two sets. Notation: X⨯Y=(x,y)|x∈X∧y∈Y.

The Cartesian product of two sets A and B is a set of all possible ordered pairs (a, b) where a is an element of A and b is an element of B.

意味（1）

(set theory) The set of all possible pairs of elements whose components are members of two sets. Notation: X⨯Y=(x,y)|x∈X∧y∈Y.

意味（2）

(databases) All possible combinations of rows between all of the tables listed.

意味（3）

(geometry) The set of points in an (m + n)-dimensional Cartesian space corresponding to all possible pairs of points from the two sets from spaces of dimension m and n. Notation: X⨯Y=(x_1,...x_m,y_1,...y_n)|(x_1,...x_m)∈X∧(y_1,...y_n)∈Y.

On the Cartesian product of two manifolds a differentiable structure can be constructed in the following way.