Solution
= Solution
The <Weierstrass approximation theorem> says that for every real <continuous function> $f$ on $[0,1]$ and every $\varepsilon>0$, there is a real <polynomial> $P$ with $\sup_{[0,1]}|f-P|<\varepsilon$. Equivalently, <polynomials> are dense in $C[0,1]$ in the <uniform norm>.