Solution
= Solution
A <best approximation> to $x$ from $U_n$ is an element $u_*\in U_n$ satisfying $\boxed{\|x-u_*\|=\inf_{u\in U_n}\|x-u\|}$. This is a <local minimum>[minimum] over the specified approximation subspace, not over all of $H$.
= Solution
A <best approximation> to $x$ from $U_n$ is an element $u_*\in U_n$ satisfying $\boxed{\|x-u_*\|=\inf_{u\in U_n}\|x-u\|}$. This is a <local minimum>[minimum] over the specified approximation subspace, not over all of $H$.