Let $O(n)$ to be the orthogonal group, and define $m(A)$ for every $A \in O(n)$ as follows: $m(A) = \max \left\{ \frac{|Ax-x|}{|x|} : x \in \mathbb{R} ^ n -\{0\} \right\}\;.$ Given a sequence $ \{B_i \}$ , we can assume by compactness that it converges.
Why does this imply that for every $\epsilon>0$ there exist $i
Thanks in advance