Finite Dimensional Real Vector Space with Euclidean Norm form Normed Vector Space

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Let $\R^n$ be an $n$-dimensional real vector space.

Let $\norm {\, \cdot \,}_2$ be the Euclidean norm.

Then $\struct {\R^n, \norm {\, \cdot \,}_2}$ is a normed vector space.


We have that:

Real Vector Space is Vector Space
By Euclidean Space is Normed Vector Space, $\norm {\, \cdot \,}_2$ is a norm on $\R^n$

By definition, $\struct {\R^n, \norm {\, \cdot \,}_2}$ is a normed vector space.