Cartesian product
In mathematics, a Cartesian product is a mathematical operation which returns a set (or product set or simply product) from multiple sets.
Description
That is, for sets A and B, the Cartesian product A × B is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B. Products can be specified using set-builder notation.
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).
More generally, a Cartesian product of n sets, also known as a n-fold Cartesian product, can be represented by an array of n dimensions, where each element is an n-tuple. An ordered pair is a 2-tuple or couple.
The Cartesian product is named after René Descartes, whose formulation of analytic geometry gave rise to the concept, which is further generalized in terms of direct product.
See also
- Analytic geometry
- Binary relation
- Concatenation of sets is deceptively similar but different concept
- Coproduct
- Exponential object
- Empty product
- Euclidean space
- Finitary relation
- Join (SQL), § Cross join
- Operation (mathematics)
- Orders on Rn
- Product (category theory)
- Product topology
- Product type
- Mathematician
- Mathematics
- René Descartes
- Set (mathematics)
- Ultraproduct
External links
- Cartesian product @ Wikipedia
