Stone–Weierstrass theorem

In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval [a, b] can be uniformly approximated as closely as desired by a polynomial function. Because polynomials are among the simplest functions, and because computers can directly evaluate polynomials, this theorem has both practical and theoretical relevance, especially in polynomial interpolation.

Source: Wikipedia — Stone–Weierstrass theorem (CC BY-SA 4.0)