Solution
= Solution
The residual is <orthogonal> to $q\in\Pi_k$, so Pythagoras gives
$$
\|f\|^2=\|q\|^2+\|f-q\|^2\ge\|q\|^2.
$$
Taking nonnegative square roots proves $\boxed{\|q\|\le\|f\|}$.
= Solution
The residual is <orthogonal> to $q\in\Pi_k$, so Pythagoras gives
$$
\|f\|^2=\|q\|^2+\|f-q\|^2\ge\|q\|^2.
$$
Taking nonnegative square roots proves $\boxed{\|q\|\le\|f\|}$.