Weierstrass' theorem

Weierstrass' theorem is an interesting theorem that says that any continuous function can be approximated arbitrarily well by polynomials (Th 2.3.4 ).

To compare with Taylor series, which also approximates continuous functions; Weierstrass' does not require differentiability. Taylor series, however, is able to give approximation coefficients at the assuming differential functions. Obtaining approximation coefficients is not trivial with Weierstrass' theorem.