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

Theorem
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.

Proof
We have that:


 * Real Vector Space is Vector Space


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

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