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:
“In old times people used to try and square the circle; now they try and devise schemes for satisfying the Irish nation.”
—Samuel Butler (1835–1902)
“...I am who I am because I’m a black female.... When I was health director in Arkansas ... I could talk about teen-age pregnancy, about poverty, ignorance and enslavement and how the white power structure had imposed it—only because I was a black female. I mean, black people would have eaten up a white male who said what I did.”
—Joycelyn Elders (b. 1933)