If $f(x)$ is continuous function on $[a,b]\Rightarrow\exists <P_{n}(x)>$ sequence of polynomials such that $P_{n}(x)$ uniformly converges to $f(x)$ on $[a,b]$. Is this statement true or false? Prove why?
This question came in an exam yesterday and I am ashamed to say that I didn't answer it because I didn't understand it. Could someone please explain this to me and whether its true or false.
Thank you.