Weierstrass Approximation Theorem

Theorem
Let $f$ be a real function which is continuous on the closed interval $\Bbb I = \closedint a b$.

Then $f$ can be uniformly approximated on $\Bbb I$ by a polynomial function to any given degree of accuracy.

Also known as
This result is also seen referred to as Weierstrass's theorem, but as there are a number of results bearing 's name, it makes sense to be more specific.