Cartesian product

Also known as direct product of sets, Cartesian product of sets, direct product, product of sets

set of the ordered pairs such that the first element of the pair is in the first element of the product and the second element of the pair is in the second element of the product

AI overview

A Cartesian product is a mathematical operation that combines two sets by creating all possible pairs, where the first item in each pair comes from the first set and the second item comes from the second set. This concept is useful because it provides a systematic way to represent all possible combinations of elements from different groups, which has applications in mathematics, computer science, and logic.

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Commons category: Set product

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Cartesian product of the sets {x,y,z} and {1,2,3}

In mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is an element of A and b is an element of B. In terms of set-builder notation, that is