\begin{definition}[Definition:Distance/Points/Normed Vector Space]
Let $\struct {X, \norm {\, \cdot \,}}$ be a normed vector space.
Let $x, y \in X$ .
Then the function $\norm {\, \cdot \,} : X \times X \to \R$:
:$\map d {x, y} = \norm {x - y}$
is called the '''distance between $x$ and $y$'''.
\end{definition}