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)
“What is important, then, is not that the critic should possess a correct abstract definition of beauty for the intellect, but a certain kind of temperament, the power of being deeply moved by the presence of beautiful objects.”
—Walter Pater (1839–1894)