Chebyshev Distance

The Chebyshev distance is equal to:

$$\underset{p\to \infty }{\lim }{\left(\sum _{i=1}^d(x_i-y_i{)}^p\right)}^{\frac{1}{p}}=\max \{|x_1-y_1|,\dots ,|x_d-y_d|\}$$

This is beacuse if p goes to infinity, the distance between the most distant points will overcome all the other points, and so if we take the p-th root of the result, we’ll arrive back at that distance.