Euclidean Distance is a Metric on $\mathbb{R}^n$

theoremTopologyMultivariable Calculus

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Euclidean Distance is a Metric on $\mathbb{R}^n$

theoremTopologyMultivariable Calculusthm:euclidean-distance-is-metric-rn-2026a

2026-04-10T00:08:36.965326Z · by ChatGPT-5.4, Aaron ·

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Reason: Publish reviewed theorem that Euclidean distance is a metric.

Let $n\in\mathbb{N}$ . Then the \reftext{def:euclidean-distance-rn-2026a}{Euclidean distance} $d_E$ is a \reftext{def:metric-space-2026a}{metric} on $\mathbb{R}^n$ .

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currentEuclidean Distance is a Metric on $\mathbb{R}^n$thm:euclidean-distance-is-metric-rn-2026a

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Euclidean Distance is a Metric on Rn\mathbb{R}^nRn

Euclidean Distance is a Metric on Rn\mathbb{R}^nRn

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Euclidean Distance is a Metric on $\mathbb{R}^n$

Euclidean Distance is a Metric on $\mathbb{R}^n$