Merge pull request #57 from upavloff/patch-5

Typo: w instead of x

chapters/statements-moonmath.tex

@@ -113,7 +113,7 @@ \subsection{Decision Functions}
 false & else
 \end{cases}
 \end{equation}
-Having defined the language $L_{3.fac}$, it then makes sense to claim the statement ``There is a word in $L_{3.fac}$". The way $L_{3.fac}$ is designed, this statement is equivalent to the statement ``There are four elements $x_1,x_2,x_3,x_4$ from the finite field $\F_{13}$ such that the equation $x_1\cdot x_2\cdot x_3 =w_4$ holds.''
+Having defined the language $L_{3.fac}$, it then makes sense to claim the statement ``There is a word in $L_{3.fac}$". The way $L_{3.fac}$ is designed, this statement is equivalent to the statement ``There are four elements $x_1,x_2,x_3,x_4$ from the finite field $\F_{13}$ such that the equation $x_1\cdot x_2\cdot x_3 =x_4$ holds.''
 
 Proving the correctness of this statement constructively means to actually find some concrete field elements that satisfy the decision function $R_{3.fac}$, like $x_1= 2$, $x_2 =12$, $x_3=4$ and $x_4 = 5$. The string $<2,12,4,5>$ is therefore a constructive proof for the statement that $L_{3.fac}$ contains words, and the computation $R_{3.fac}(<2,12,4,5>)=true$ is a verification of that proof. In contrast, the string $<2, 12, 4, 7>$ is not a proof of the statement, since the check $R_{3.fac}(<2,12,4,7>)=false$ does not verify the proof.
 \end{example}