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:
“I walked by the Union Square Bar, I was gonna go in. And I saw myself, my reflection in the window. And I thought, “I wonder who that bum is.” And then I saw it was me. Now look at me, I’m a bum. Look at me. Look at you. You’re a bum.”
—J.P. (James Pinckney)
“But the relationship of morality and power is a very subtle one. Because ultimately power without morality is no longer power.”
—James Baldwin (1924–1987)