# 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.

$\blacksquare$