diff --git a/semester3/ti-compact/parts/01_words-alphabets.tex b/semester3/ti-compact/parts/01_words-alphabets.tex
index 077b0d9..af8c06b 100644
--- a/semester3/ti-compact/parts/01_words-alphabets.tex
+++ b/semester3/ti-compact/parts/01_words-alphabets.tex
@@ -51,7 +51,9 @@ where the Program doesn't have to compile, i.e. we can describe processes inform
 
 \inlinetheorem Kolmogorov-Complexity doesn't depend on programming language. It only differs in constant
 
-\fancydef{Randomness} $x$ random if $K(x) \geq |x|$, thus for $n$, $K(n) \geq \ceil{\log_2(n + 1)} - 1$
+\fancydef{Randomness} $x \in \wordbool$ random if $K(x) \geq |x|$, thus for $n \in \N$, $K(n) \geq \ceil{\log_2(n + 1)} - 1$
 
 \stepLabelNumber{theorem}
 \fancytheorem{Prime number} $\displaystyle \limni \frac{\text{Prime}(n)}{\frac{n}{\ln(n)}}$
+
+\fhlc{Cyan}{Proofs} Most of the proofs start with defining the number of words of exactly the required length and we can then usually deduce some kind of indirect proof (using the fact that there are at most $2^n - 1$ words $x$ with $K(x) < n$).
diff --git a/semester3/ti-compact/ti-compact.pdf b/semester3/ti-compact/ti-compact.pdf
index d0fea01..da4139f 100644
Binary files a/semester3/ti-compact/ti-compact.pdf and b/semester3/ti-compact/ti-compact.pdf differ