Cartesian Product - Cartesian Square and Cartesian Power

Cartesian Square and Cartesian Power

The Cartesian square (or binary Cartesian product) of a set X is the Cartesian product X2 = X × X. An example is the 2-dimensional plane R2 = R × R where R is the set of real numbers - all points (x,y) where x and y are real numbers (see the Cartesian coordinate system).

The cartesian power of a set X can be defined as:

An example of this is R3 = R × R × R, with R again the set of real numbers, and more generally Rn.

The n-ary cartesian power of a set X is isomorphic to the space of functions from an n-element set to X. As a special case, the 0-ary cartesian power of X may be taken to be a singleton set, corresponding to the empty function with codomain X.