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.

$\blacksquare$