Cartesian Products

Ordered Pair

An ordered pair is an ordered list of mathematical objects, x and y, which is written as (x,y). The word "ordered" does imply that the order in which x and y are written matters, so \((x,y) ≠ (y,x)\) in general.

Cartesian Product

Let A and B be subsets of S. The Cartesian product(cross product) of A and B, denoted by:

A \(\times\) B = {(x,y)| x ∈ A and y ∈ B}

The cartesion product of two sets A and B is the set of all ordered paris whose first component comes from A and whose second component comes from B. Sometimes, we are interested in the cross product of a set with itself, we will abbreviate \(A \times A\) as \(A^2\).

Example

If A = {1,2} and B = {a,b,c}. Find cartesian product of \(A \times B\)
The cartesion product of sets A and B is {(1,a),(1,b),(1,c),(2,a),(2,b),(2,c)}

Pixel Coordinates Application

A digital image is made up of rows and columns of pixels. A pixel in such an image can be specified by saying which column and which row contains it. In terms of coordinates, a pixel can be identified by a pair of integers giving the column number and the row number.

Database Application

Reference

saylor academy
MathsMD