I'm reading Shannon's 1948 paper where I encountered Theorem 4:
$$ \lim \limits_{N \to \infty} \frac {\log n(q)} N = H $$
In Appendix 3 after proving Theorem 3, Shannon proves Theorem 4 by saying:
Theorem 4 follows immediately from this on calculating upper and lower bounds for n(q) based on the possible range of values of p in Theorem 3.
I don't understand how one calculates upper and lower bounds for n(q). How can p's possible range of values be used for this?