1.1 --- a/tex/theory1_ex6.tex	Mon Jun 27 01:01:33 2011 +0200
     1.2 +++ b/tex/theory1_ex6.tex	Mon Jul 04 16:41:40 2011 +0200
     1.3 @@ -70,7 +70,7 @@
     1.4  &= \sum_{i=1}^{n}\Phi_i - \sum_{i=0}^{n-1}\Phi_i + \sum_{i=1}^{n}t_i\\
     1.5  &= \Phi_n - \Phi_0 + \sum_{i=1}^{n}t_i\\
     1.6  \end{align*}
     1.7 -By definition we know that $\Phi_0 = -1$ and since $2k-s \geq 0$ for $\alpha \geq \frac{1}{2}$ and $\frac{s}{2}-k \geq 0$ for $\alpha < \frac{1}{2}$ it follows that $\Phi_n - \Phi_0 >= 0$.
     1.8 +By definition we know that $\Phi_0 = -1$ and since $2k-s \geq 0$ for $\alpha \geq \frac{1}{2}$ and $\frac{s}{2}-k \geq 0$ for $\alpha < \frac{1}{2}$ it follows that $\Phi_n - \Phi_0 \geq 0$.
     1.9  \[\implies \Phi_n - \Phi_0 + \sum_{i=1}^{n}t_i \geq \sum t_i\]\qed
    1.10  
    1.11  \section*{Exercise 6.3}