Wikipedia: History of Cartesian product

Difference (from prior major revision) (minor diff, author diff)

Changed: 1c1

If two sets, X and Y, are defined, then we can define the Cartesian product of the two sets, XY, as the set of ordered pairs with the first element of each pair selected from X and the second element selected from Y.

Given two sets X and Y, the Cartesian product (or direct product) of the two sets, written as X × Y is the set of all ordered pairs with the first element of each pair selected from X and the second element selected from Y.

Changed: 3c3

:XY = {<x,y> | x belongs to X and y belongs to Y}

:X × Y = { (x,y) | x in X and y in Y }

Changed: 5c5,15

back to Mathematics -- Set Theory

For example, if set X is the 13-element set {A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2} and set Y is the 4-element set {spades, hearts, diamonds, clubs}, then the Cartesian product of those two sets is the 52-element set { <A, spades>, <K, spades>, ... <2, spades>, <A, hearts>, ... <3, clubs>, <2, clubs> }. Another example is the 2-dimensional plane R × R where R is the set of real numbers. Subsets of the Cartesian product are called binary relations.

The binary Cartesian product can be generalized to the n-ary Cartesian product over n sets X₁,... ,X_n:

:X₁ × ... × X_n = { (x₁,... ,x_n) | x₁ in X₁ and ... and x_n in X_n }

An example of this is the Euclidean 3-space R × R × R, with R again the set of real numbers.

The Cartesian product is named after Rene Descartes whose formulation of analytic geometry gave rise to this concept.

See also Mathematics -- Set theory

	Revision 16 . . (edit) December 4, 2001 4:53 am by (logged).109.166.xxx
	Revision 15 . . (edit) September 30, 2001 9:27 pm by Zundark [fix link]
	Revision 1 . . (edit) June 29, 2001 8:48 pm by Larry Sanger