Euclidean Space without Origin is Path-Connected

Theorem
Let $n \in \Z: n \ge 2$.

Let $\R^n$ be the $n$-dimensional Euclidean space.

Let $\R^n \setminus \set {\mathbf 0}$ be $\R^n$ with the origin removed.

Then $\R^n \setminus \set {\mathbf 0}$ is path-connected.