Weierstraß's Polynomial Theorem

A function, continuous in a finite close interval, can be approximated with a preassigned accuracy by Polynomials. A function of a Real variable which is continuous and has period $2\pi$ can be approximated by trigonometric Polynomials.

References

Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., p. 5, 1975.