### Definition of Cartesian product

**1.** *Noun.* The set of elements common to two or more sets. "The set of red hats is the intersection of the set of hats and the set of red things"

### Definition of Cartesian product

**1.** Noun. (set theory) The set of all possible pairs of elements whose components are members of two sets. Notation: $X\; \backslash times\; Y\; =\; \backslash \{(x,y)\backslash \; x\backslash in\; X\; \backslash land\; y\backslash in\; Y\backslash \}$. ¹

¹ *Source: wiktionary.com*

### Cartesian Product Pictures

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### Lexicographical Neighbors of Cartesian Product

### Literary usage of Cartesian product

Below you will find example usage of this term as found in modern and/or classical literature:

**1.** *Statistics and Science: A Festschrift for Terry Speed* by Darlene Renee Goldstein, Terry Speed (2003)

"... containing a given (innately transitive) subgroup G is finding all ways of
identifying Q with a **cartesian product** Te with ..."**2.** *Base SAS(R) 9.1.3 Procedures Guide, Second Edition, Volumes 1-4* by Sas Institute (2006)

"The **cartesian product** is the result of combining every row from one table ...
You get the **cartesian product** when you join two tables and do not subset them ..."**3.** *SAS(R) 9.1 SQL Procedure User's Guide* by SAS Institute, Institute SAS Institute (2004)

"When you run this query, the following message is written to the SAS log: Output
3.3 **cartesian product** Log Message NOTE: The execution of this query ..."**4.** *Doing More with SAS/Assist 9.1* by SAS Institute, Institute SAS Institute (2004)

"Combining Data Using a **cartesian product** Match Merge You can use Combine on the
Data Management menu to combine your data in several ways. ..."**5.** *Distributions with Fixed Marginals and Related Topics* by B. (Berthold) Schweizer, Ludger RÃ¼schendorf, Michael Dee Taylor (1996)

"... whose domain is the closure of that of C' (hence the domain of C" is the
**cartesian product** of n closed subsets of /). If the domain of C" is all of /n, ..."