Cartesian product
Noun
Meaning
the set of elements common to two or more sets
Source: WordNetSynonyms
Hypernyms
Examples
the set of red hats is the intersection of the set of hats and the set of red things
All three can similarly be defined for the Cartesian product of more than two sets.
A relation from a domain A to a codomain B is a subset of the Cartesian product A × B. Given this concept, we are quick to see that the set F of all ordered pairs (x, x 2 ), where x is real, is quite familiar.
¡ Apply the link to the left once if ¬ returned a non-empty array, zero timed if it returned 0. $ Monadic chain: ߀ Map the main link over x. Œp Take the Cartesian product.
;Column order significance :The order of columns in an SQL table is defined and significant, one consequence being that SQL's implementations of Cartesian product and union are both noncommutative.
In analogy to the product order this is the product direction on the Cartesian product.