From 61a9006feaad27304d52b066cab77511af78a207 Mon Sep 17 00:00:00 2001
From: upavloff <32176478+upavloff@users.noreply.github.com>
Date: Thu, 2 Mar 2023 14:39:18 +0100
Subject: [PATCH] Typo: w instead of x

---
 chapters/statements-moonmath.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/chapters/statements-moonmath.tex b/chapters/statements-moonmath.tex
index b031a420..e46006ab 100644
--- a/chapters/statements-moonmath.tex
+++ b/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}