If $ f $ is a continuous real-valued function on a interval $ [a,b] $ then for all $ \varepsilon>0 $ there exists a polynomial $ P $ which satisfies $ |f(x)-P(x)|<\varepsilon \quad \forall x\in [a,b] $ This theorem also holds for compact subsets of $ \Bbb{R}^n . $ The Stone-Weierstrass theorem is a generalization to even more general situations.