# Cartesian product

## Mathematical set formed from two given sets / From Wikipedia, the free encyclopedia

#### Dear Wikiwand AI, let's keep it short, summarize this topic like I'm... Ten years old or a College student

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 in *A* and *b* is in *B*.[1] In terms of set-builder notation, that is

A table can be created by taking the Cartesian product of a set of rows and a set of columns. If the Cartesian product *rows* × *columns* is taken, the cells of the table contain ordered pairs of the form (row value, column value).[4]

One can similarly define the Cartesian product of *n* sets, also known as an ** n-fold Cartesian product**, which can be represented by an

*n*-dimensional array, where each element is an

*n*-tuple. An ordered pair is a 2-tuple or couple. More generally still, one can define the Cartesian product of an indexed family of sets.

The Cartesian product is named after René Descartes,[5] whose formulation of analytic geometry gave rise to the concept, which is further generalized in terms of direct product.