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changeset 15:2c32ba8308c3

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hopefully fix compilation error in funktionen unit
author Markus Kaiser <markus.kaiser@in.tum.de>
date Wed, 06 Nov 2013 13:54:00 +0100
parents af55ae8de0d7
children b83150706135
files notes/tex/basics.tex
diffstat 1 files changed, 60 insertions(+), 60 deletions(-) [+]
line wrap: on
line diff
--- a/notes/tex/basics.tex	Tue Nov 05 00:41:39 2013 +0100
+++ b/notes/tex/basics.tex	Wed Nov 06 13:54:00 2013 +0100
@@ -493,88 +493,88 @@
     Dabei bezeichnet $id$ die \structure{Identität} mit $id(x) \defeq x$.
 \end{frame}
 
-\begin{frame}
-    \frametitle{Eigenschaften von Funktionen}
-    \setbeamercovered{dynamic}
+{
+    \tikzstyle{set} = [draw, thick, tumgreen, fill=tumgreen!15]
+    \tikzstyle{element} = [thick]
+    \tikzstyle{head} = [draw, fill=tumblue!15, thick]
+    \tikzstyle{arrow} = [thick, tumblue, shorten >=-.4em, shorten <=-.4em]
+    \newcommand{\function}[3]{%
+        \draw[set] (0, 0) ellipse (1 and 2);
+        \draw[set] (4, 0) ellipse (1 and 2);
 
-    \begin{block}{Eigenschaften von Funktionen}
-        Sei $f: A \to B$ eine Funktion. Man nennt $f$
-        \begin{description}[surjektiv]
-            \item[injektiv] $\forall b \in B. \abs{f^{-1}(b)} \leq 1$ \hfill(Kein $b$ wird doppelt getroffen)
-            \item[surjektiv] $\forall b \in B. \abs{f^{-1}(b)} \geq 1$\hfill(Jedes $b$ wird getroffen)
-            \item[bijektiv] $\forall b \in B. \abs{f^{-1}(b)} = 1$\hfill(Jedes $b$ wird genau einmal getroffen)
-        \end{description}
-    \end{block}
-
-    \vfill
-    \centering
-    {
-        \tikzstyle{set} = [draw, thick, tumgreen, fill=tumgreen!15]
-        \tikzstyle{element} = [thick]
-        \tikzstyle{head} = [draw, fill=tumblue!15, thick]
-        \tikzstyle{arrow} = [thick, tumblue, shorten >=-.4em, shorten <=-.4em]
-        \newcommand{\function}[3]{%
-            \draw[set] (0, 0) ellipse (1 and 2);
-            \draw[set] (4, 0) ellipse (1 and 2);
+        \path[element]
+        (0,0)
+        +(0, 1.5) node (a1) {$\times$}
+        +(0.2, 0.85) node (a2) {$\times$}
+        +(0.1, 0.3) node (a3) {$\times$}
+        +(-0.1, -0.1) node (a4) {$\times$}
+        +(-0.2, -0.7) node (a5) {##2}
+        +(-0.1, -1.5) node (a6) {##3};
 
-            \path[element]
-                (0,0)
-                +(0, 1.5) node (a1) {$\times$}
-                +(0.2, 0.85) node (a2) {$\times$}
-                +(0.1, 0.3) node (a3) {$\times$}
-                +(-0.1, -0.1) node (a4) {$\times$}
-                +(-0.2, -0.7) node (a5) {#2}
-                +(-0.1, -1.5) node (a6) {#3};
+        \path[element]
+        (4,0)
+        +(0, 1.5) node (b1) {$\times$}
+        +(0.2, 0.85) node (b2) {$\times$}
+        +(-0.3, 0.0) node (b3) {$\times$}
+        +(0.1, -0.6) node (b4) {$\times$}
+        +(-0.1, -1.5) node (b5) {$\times$};
+
+        \path
+        (0, -2.5) node {$A$}
+        (4, -2.5) node {$B$}
+        (2, -2.5) node {$f$}
+        (2, 3) node[head] {##1};
+    }
 
-            \path[element]
-                (4,0)
-                +(0, 1.5) node (b1) {$\times$}
-                +(0.2, 0.85) node (b2) {$\times$}
-                +(-0.3, 0.0) node (b3) {$\times$}
-                +(0.1, -0.6) node (b4) {$\times$}
-                +(-0.1, -1.5) node (b5) {$\times$};
+    \begin{frame}
+        \frametitle{Eigenschaften von Funktionen}
+        \setbeamercovered{dynamic}
 
-            \path
-                (0, -2.5) node {$A$}
-                (4, -2.5) node {$B$}
-                (2, -2.5) node {$f$}
-                (2, 3) node[head] {#1};
+        \begin{block}{Eigenschaften von Funktionen}
+            Sei $f: A \to B$ eine Funktion. Man nennt $f$
+            \begin{description}[surjektiv]
+                \item[injektiv] $\forall b \in B. \abs{f^{-1}(b)} \leq 1$ \hfill(Kein $b$ wird doppelt getroffen)
+                \item[surjektiv] $\forall b \in B. \abs{f^{-1}(b)} \geq 1$\hfill(Jedes $b$ wird getroffen)
+                \item[bijektiv] $\forall b \in B. \abs{f^{-1}(b)} = 1$\hfill(Jedes $b$ wird genau einmal getroffen)
+            \end{description}
+        \end{block}
 
-        }
+        \vfill
+        \centering
         \begin{tikzpicture}[x=1.5em, y=1.5em]
             \function{Injektiv}{}{}
 
             \path[arrow]
-                (a1) edge (b1)
-                (a2) edge (b3)
-                (a3) edge (b2)
-                (a4) edge (b4);
+            (a1) edge (b1)
+            (a2) edge (b3)
+            (a3) edge (b2)
+            (a4) edge (b4);
         \end{tikzpicture}
         \hfill
         \begin{tikzpicture}[x=1.5em, y=1.5em]
             \function{Surjektiv}{$\times$}{$\times$}
 
             \path[arrow]
-                (a1) edge (b1)
-                (a2) edge (b3)
-                (a3) edge (b2)
-                (a4) edge (b4)
-                (a5) edge (b5)
-                (a6) edge (b5);
+            (a1) edge (b1)
+            (a2) edge (b3)
+            (a3) edge (b2)
+            (a4) edge (b4)
+            (a5) edge (b5)
+            (a6) edge (b5);
         \end{tikzpicture}
         \hfill
         \begin{tikzpicture}[x=1.5em, y=1.5em]
             \function{Bijektiv}{}{$\times$}
 
             \path[arrow]
-                (a1) edge (b1)
-                (a2) edge (b3)
-                (a3) edge (b2)
-                (a4) edge (b4)
-                (a6) edge (b5);
+            (a1) edge (b1)
+            (a2) edge (b3)
+            (a3) edge (b2)
+            (a4) edge (b4)
+            (a6) edge (b5);
         \end{tikzpicture}
-    }
-\end{frame}
+    \end{frame}
+}
 }
 
 \defineUnit{aussagenlogiksyntax}{%