Questions tagged [weierstrass-approximation]
For questions about or using the Weierstrass approximation theorem (or the Stone-Weierstrass theorem). The Weierstrass theorem states that if $f:[a,b]\to\mathbb R$ is continuous and if $\epsilon>0$, then there exists a polynomial $p$ such that $$ |f(x)-p(x)|<\epsilon $$ for all $x$ in $[a,b]$. In words, any continuous function on a closed and bounded interval can be uniformly approximated on that interval by polynomials to any degree of accuracy.