Merge pull request #51 from Danghor/master

Fix typos

Author: karlstroetmann

Lecture-Notes/limits.tex

@@ -187,7 +187,7 @@ \section{The Halting Problem}
 \end{Theorem}
 
 \noindent
-\textbf{Proof}:  In order to prove the undecidabilty of the halting problem we have to show that
+\textbf{Proof}:  In order to prove the undecidability of the halting problem we have to show that
 there can be no function \texttt{stops} satisfying the specification given above.  This calls for an
 indirect proof also known as \href{http://en.wikipedia.org/wiki/Indirect_proof}{\emph{proof by contradiction}}.
 We will therefore assume that a function \texttt{stops} solving the halting problem does
@@ -306,7 +306,7 @@ \section{The Halting Problem}
 \cite{turing:36}.  Of course, Turing did not solve the problem for \textsc{SetlX} but rather
 for the so called 
 \href{http://en.wikipedia.org/wiki/Indirect_proof}{\emph{Turing machines}}.  
-A \emph{Turing maschine} can be interpreted as a formal description of an algorithm.  
+A \emph{Turing machine} can be interpreted as a formal description of an algorithm.  
 Therefore, Turing has shown, that there is no algorithm that is able to decide whether some given
 algorithm will always terminate.
 \vspace*{0.3cm}