Taxicab Metric on Real Vector Space is Metric/Proof 1

Theorem

The taxicab metric on the real vector space $\R^n$ is a metric.

Proof

This is an instance of the taxicab metric on the cartesian product of $A_{1'}, A_{2'}, \ldots, A_{n'}$.

This is proved in Taxicab Metric is Metric.

$\blacksquare$