Taxicab Metric on Real Vector Space is Metric/Proof 1
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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.
$\blacksquare$