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# Def/Euclidean metric

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Definition of Euclidean metric: Suppose that $n$ is a positive natural number. The Euclidean metric on the real vector space $\RR^n$ is the following "distance function":

• For all $\vec v, \vec w \in \RR^n$, the Euclidean distance between $\vec v$ and $\vec w$ is given by:

$$d(\vec v, \vec w) = \sqrt{ \sum_{i=1}^n (v_i - w_i)^2 }.$$

## Logical Connections

This definition logically relies on the following definitions and statements: Def/Real number, Def/Vector space

The following statements and definitions logically rely on the material of this page: Struct/Half open square

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