Deformation retraction confusion

Question

I am looking at the retraction deformations and one I saw is $r: R^n \to E^n$ and $$r(x) = \begin{cases} \dfrac{x}{|x|} & |x| \geq 1 \\ x & 0\leq |x|\leq 1 \end{cases} .$$ How does $r(x)$ go from $R^n$ to $E^n$ if $x$ is a number?

Answer 1

$x$ is not a number, $x$ is a vector in $\mathbb{R}^n$. However, $|x|$ is a number, which is why it's ok to say $|x| \ge 1$ and $0 \le |x| \le 1$.