# Cartesian product

In mathematics, sets can be used to make new sets. Given two sets A and B, the Cartesian product of A with B is written as A × B,[1] and is the set of all ordered pairs whose first element is a member of A, and whose second element is a member of B.[2]

For example, let A = {1, 2, 3} and B = {a, b}. Then:

${\displaystyle A\times B=\{(1,a),(1,b),(2,a),(2,b),(3,a),(3,b)\}}$

The set of a Cartesian product can be visualized as a two-dimensional table, with its entry being its elements.[3]

## References

1. "Comprehensive List of Set Theory Symbols". Math Vault. 2020-04-11. Retrieved 2020-09-05.
2. Weisstein, Eric W. "Cartesian Product". mathworld.wolfram.com. Retrieved 2020-09-05.
3. "Cartesian Product". web.mnstate.edu. Archived from the original on 2020-07-18. Retrieved 2020-09-05.