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.
Read more about this topic: Cartesian Product
Famous quotes containing the words square and/or power:
“Houses haunt me.
That last house!
How it sat like a square box!”
—Anne Sexton (1928–1974)
“O power of fantasy that steals our minds from things outside, to leave us unaware, although a thousand trumpets may blow loud—what stirs you if the senses show you nothing? Light stirs you, formed in Heaven, by itself, or by His will Who sends it down to us.”
—Dante Alighieri (1265–1321)