Real Numbers with Absolute Value form Normed Vector Space

Theorem
Let $\R$ be the set of real numbers.

Let $\size {\, \cdot \,}$ be the absolute value.

Then $\struct {\R, \size {\, \cdot \,}}$ is a normed vector space.

Proof
We have that:


 * Real Numbers form Vector Space


 * Absolute Value is Norm

By definition, $\struct {\R, \size {\, \cdot \,}}$ is a normed vector space.