Taxicab metric

Example

Let $n \ge 1$ be an integer. For $x = (x_1, \ldots, x_n)$ and $y = (y_1, \ldots, y_n)$ in $\mathbb{R}^n$, let $$d_1(x, y) = \sum_{i=1}^{n} |x_i - y_i|.$$ Then $d_1$ is a metric on $\mathbb{R}^n$, the taxicab metric.