I'm not a mathematician, but these two theorems sound related to me.
Taylor's theorem. Every k-times differentiable function can be approximated in a neighborhood around a given point by a k-th order polynomial to an arbitrary degree.
Weierstrass theorem. Every continuous function defined on a closed interval $[a, b]$ can be approximated to an arbitrary degree by a polynomial function.
(The statements are probably not precise.) I always wondered what is the underlying relationship between those two? Does one imply the other, or are they each special cases of some more general result?