I've been reading the book in parallel with watching the lectures. I think that equation 2.13 on page 57 is wrong or perhaps just misleading. The expression right before equation 2.13 is of the form

N >= const * ln(m(2N)) for fixed eps and delta.

Then equation 2.10, m(N) <= 1+N^d_vc, is used to rewrite the expression as equation 2.13, N >= const * ln(1+(2N)^d_vc)

But all we can really say from these two expressions is

N >= const * ln(m(2N)) <= const * ln(1+(2N)^d_vc)

In other words, I don't see how I can know the sign of the inequality "?" in

N ? const * ln(1+(2N)^d_vc)

What am I missing

This seems an important thing, so please help me see my error....