Cartesian Product Operation
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A Cartesian Product Operation is a Set Operation that returns a product set from multiple sets.
- AKA: ×.
- Counter-Example(s):
- See: Multiplication Operation, Empty Set, Ordered Pairs, Tuple.
References
2014
- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/cartesian_product Retrieved:2014-8-3.
- In mathematics, a Cartesian product is a mathematical operation which returns a set (or product set) from multiple sets. That is, for sets A and B, the Cartesian product is the set of all ordered pairs where and .
The simplest case of a Cartesian product is the Cartesian square, which returns a set from two sets. A table can be created by taking the Cartesian product of a set of rows and a set of columns. If the Cartesian product is taken, the cells of the table contain ordered pairs of the form .
A Cartesian product of n sets can be represented by an array of n dimensions, where each element is an n-tuple. An ordered pair is a 2-tuple.
The Cartesian product is named after René Descartes, [1] whose formulation of analytic geometry gave rise to the concept.
- In mathematics, a Cartesian product is a mathematical operation which returns a set (or product set) from multiple sets. That is, for sets A and B, the Cartesian product is the set of all ordered pairs where and .
- ↑ cartesian. (2009). In Merriam-Webster Online Dictionary. Retrieved December 1, 2009, from http://www.merriam-webster.com/dictionary/cartesian