Euclidean Metric on Real Vector Space is Metric/Proof 1
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Theorem
The Euclidean metric on a real vector space $\R^n$ is a metric.
Proof
The Euclidean metric on $\R^n$ is a special case of the $p$-product metric.
The result follows from $p$-Product Metric on Real Vector Space is Metric.
$\blacksquare$