Cartesian Product

From Math Images

Revision as of 11:12, 27 September 2009 by AnnaP (Talk | contribs)
(diff) ←Older revision | Current revision (diff) | Newer revision→ (diff)
Jump to: navigation, search
This is a Helper Page for:
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  A \times B is different from  B \times A . In the former, the elements of A are listed first, and in the latter, the elements of B are listed first.

An example is  \{1,4,6\} \times \{2,9\} = \{ (1,2), (1,9), (4,2), (4, 9), (6,2), (6,9)\}


Note that this is different from  \{2,9\} \times  \{1,4,6\} = \{ (2,1), (2,4), (2,6), (9,1), (9,4), (9,6)\} .


Another example is  \{a,b,c\} \times \{2, 5\} = \{(a,2), (a, 5), (b,2), (b,5), (c,2), (c, 5)\}


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.

Personal tools