## Cartesian product

Cartesian product of two sets S and T. The set of all ordered pairs of the form (s,t) with the property that s is a member of S and t is a member of T; this is usually written as S × T. Formally, S × T = {(s,t)|(sS) and (t T)}

If R denotes the set of real numbers, then R × R is just the set of points in the (Cartesian) plane or it can be regarded as the set of complex numbers, hence the name.

The concept can be extended to deal with the Cartesian product of n sets, S1,S2,…,Sn

This is the set of ordered n-tuples (s1,s2,…,sn)

with the property that each si is in Si. In the case where each Si is the same set S, it is customary to write Sn for S × S × … S (n terms)

Pick a style below, and copy the text for your bibliography.

• MLA
• Chicago
• APA

"Cartesian product." A Dictionary of Computing. . Encyclopedia.com. 19 Mar. 2019 <https://www.encyclopedia.com>.

"Cartesian product." A Dictionary of Computing. . Encyclopedia.com. (March 19, 2019). https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/cartesian-product

"Cartesian product." A Dictionary of Computing. . Retrieved March 19, 2019 from Encyclopedia.com: https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/cartesian-product

### Citation styles

Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).

Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.

Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:

#### Modern Language Association

http://www.mla.org/style

#### The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

#### American Psychological Association

http://apastyle.apa.org/

##### Notes:
• Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
• In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.