For any positive integer , the norm is a class of distance measures given as
where is the absolute value. In the general form given above, it is also called the -order Minkowski distance.
As , the norm approaches the largest coordinate distance between the two points. In general, we only care about the norm (Manhattan distance), the norm (Euclidean distance), and norm (Chebyshev distance).
Consider, for example, the vectors and . Then