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zwYZWK`>&U-uo?C3{{mwHoc^F6LdDBkkk%}dsw6=M>ly1H^=8l|6i79La5Y4VC5cnBL9D=Yfjd|?M{QdH+%4#EHo!4?>1 zg0>3#ZFcwed=>NWDu=SEc7q zou;Hub57T!Uq76#OMlv(ZYZ01<#bcoeAVfevfrPbZYv*Z>~cr>^r+KaDe+yUPUr#-KKbA|^W-nPrsCb~@*gnwE&c-yjziy<+}8vh3@|b< MGBye&B}Gq03eE}basU7T diff --git a/main.tex b/main.tex index 1f474a4..546a290 100644 --- a/main.tex +++ b/main.tex @@ -18,6 +18,9 @@ \newcommand{\integers}{\mathbb{Z}} \newtheorem{defi}{Definition} +\newtheorem{koro}{Korollar} +\newtheorem{lemma}{Lemma} +\newtheorem{satz}{Satz} \newtheorem*{beis}{Beispiel} @@ -155,6 +158,34 @@ das allgemeine \(n\)-Kaffee-Problem formulieren. oder umgekehrt. \end{defi} +Betrachtet man die Anforderung an die Kaffeekasse, +dass die Summe über die Kaffee-Deltas \(0\) sein soll, +fällt eine Vereinfachungsmöglichkeit auf. + +\begin{satz} + Um das \(n\)-Kaffee-Problem zu lösen + genügt eine \((n-1)\)-Kaffeekasse. +\end{satz} +\begin{proof} + Ist noch zu formulieren. +\end{proof} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Bilanzierende Kaffeekassen und das Kaffee-Paradoxon +\subsection{Bilanzierende Kaffeekassen und das Kaffee-Paradoxon} +\label{sub:kaffeeparadoxon} + +\todo[inline]{Die Unterscheidung zwischen bilanzierenden und expliziten Kaffeekassen einführen. +Das Kaffeeparadoxon beschreiben und auflösen.} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Visualisierung des Kaffeeproblems +\section{Visualisierung des Kaffeeproblems} +\label{sec:visualisierung} + \begin{beis}[2-Kaffee-Problem] Sind nur 2 Personen \( p_0 \) und \( p_1 \) an der Kaffeerunde beteiligt, lässt sich das 2-Kaffee-Problem als \( x \in \mathbb{Z} \) beschreiben. Hierbei gilt: \begin{description} @@ -182,23 +213,6 @@ das allgemeine \(n\)-Kaffee-Problem formulieren. Diese Kaffeefunktion \( k_i \) gibt die Veränderung der Guthaben-Schulden-Verhältnisse innerhalb der Kaffeerunde an, wenn \( p_i \) ein Kaffee \textbf{ausgegeben wird}. \end{defi} -\begin{beis}[3-Kaffee-Problem] -\todo{Text ergänzen} - \begin{figure}[hbtp] - \centering - \includegraphics[scale=1]{3KaffeeProblem} - \caption{} - \end{figure} -\end{beis} - - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Visualisierung des Kaffeeproblems -\section{Visualisierung des Kaffeeproblems} -\label{sec:visualisierung} - -