I am reading An Introduction to Algebraic Topology by Rotman. After proving
Theorem 2.7: For every $k\geq 0$, euclidean space$\mathbb R^n$ contains $k$ points in general position,
the book remarked: There are other proofs of this theorem using induction on k. The key geometric observation needed is that $\mathbb R^n$ is not the union of only finitely many proper affine subsets . I want to prove that observation.