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1
vote
bracketing number vs covering number
$$
\begin{aligned}
\|f - (l+u)/2\| & = \| (f - l)/2 - (u - f)/2 \| \\
& \le \max \left\{ \frac{1}{2} \|f-l\| ,\frac{1}{2} \|u - f\| \right\}\\
& \le \frac{1}{2} \|u-l\| \\
&\le\epsilon.
\end{aligned}$ …