An ambiguity in SVM equations about misclassified data
Good point! Interesting consequence!

Problem is the $a_n=0$ assumption, i.e. assuming misclassified points are not support vectors.

Here is the flow. Slack variable $\xi_n$ is defined as 
$$\xi_n := |t_n - y(\boldsymbol{x}_n)|$$
where $t_n \in \{+1, -1\}$ is the true label, and $y(\boldsymbol{x}_n)$ is the prediction. Therefore, for a misclassified point (on the wrong side) we have $$\xi_n &gt; 1$$ by definition. Given $\mu_n \xi_n = 0$, therefore$$\mu_n=0$$
and given $a_n=C - \mu_n$, therefore $$a_n = C &gt; 0$$ which means (given $a_n &gt; 0$ only for support vectors)


  Every misclassified  point is a support vector.


This is a nice consequence and should have been stated in the book. 

Although, a remotely! related point has been stated in the book:


  Points with $a_n = C$ can lie inside the margin and can either be
  correctly classified if $\xi_n \leq 1$ or misclassified if $\xi_n &gt; 1$.