If f is a continuous real-valued function on [a, b] and if any ϵ>0 is given, then there exists a polynomial p on [a, b] such that left bracketing bar f(x) - P(x) right bracketing bar <ϵ for all x element [a, b]. In words, any continuous function on a closed and bounded interval can be uniformly approximated on that interval by polynomials to any degree of accuracy.

Müntz's theorem | Stone-Weierstrass theorem

Karl Weierstrass