| 释义 |
Cartesian product
Cartesian productn. A set of all pairs of elements (x, y) that can be constructed from given sets, X and Y, such that x belongs to X and y to Y.Cartesian product n 1. (Mathematics) maths logic the set of all ordered pairs of members of two given sets. The product A × B is the set of all pairs <a, b> where a is a member of A and b is a member of B. Also called: cross product 2. (Logic) maths logic the set of all ordered pairs of members of two given sets. The product A × B is the set of all pairs <a, b> where a is a member of A and b is a member of B. Also called: cross product Thesaurus| Noun | 1. | Cartesian product - the set of elements common to two or more sets; "the set of red hats is the intersection of the set of hats and the set of red things"intersection, productset - a group of things of the same kind that belong together and are so used; "a set of books"; "a set of golf clubs"; "a set of teeth" |
TranslationsCartesian product
cartesian product[kär′tē·zhan ′präd·əkt] (mathematics) In reference to the product of P and Q, the set P × Q of all pairs (p,q), where p belongs to P and q belongs to Q. Cartesian product (mathematics)(After Renee Descartes, French philosper andmathematician) The Cartesian product of two sets A and B isthe set
A x B = a, b) | a in A, b in .
I.e. the product set contains all possible combinations of oneelement from each set. The idea can be extended to productsof any number of sets.
If we consider the elements in sets A and B as points alongperpendicular axes in a two-dimensional space then theelements of the product are the "Cartesian coordinates" ofpoints in that space.
See also tuple.Cartesian product
Synonyms for Cartesian productnoun the set of elements common to two or more setsSynonymsRelated Words |