|Projection of a Torus|
The Cartesian Product is a particular way of combining two sets. If we have two sets A and B, the Cartesian product is the set of all ordered pairs created by listing an arbitrary element of A first, then an element of B. Note that order matters here, and the Cartesian Product is different from . In the former, the elements of A are listed first, and in the latter, the elements of B are listed first.
An example is
Note that this is different from .
Another example is
A more abstract example is the complex numbers can be thought of as the Cartesian product of the real numbers with the imaginary numbers. The first component of a complex number is its real part, and the second component is its imaginary part.