Mercurial > 13ws.ds
comparison notes/tex/basics.tex @ 21:03a0cf37ddaa
fix compilation errors
| author | Markus Kaiser <markus.kaiser@in.tum.de> |
|---|---|
| date | Mon, 18 Nov 2013 15:20:06 +0100 |
| parents | d9b98c2ba5ac |
| children | 4436f8006ebd |
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| 20:d9b98c2ba5ac | 21:03a0cf37ddaa |
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| 107 \item[$A \cap B$] $\defeq \left\{ x \mid x \in A\ \text{und}\ x \in B \right\}$\hfill\alert{Schnitt} | 107 \item[$A \cap B$] $\defeq \left\{ x \mid x \in A\ \text{und}\ x \in B \right\}$\hfill\alert{Schnitt} |
| 108 \item[$A \setminus B$] $\defeq A \cap \setnot{B}$\hfill\alert{Differenz} | 108 \item[$A \setminus B$] $\defeq A \cap \setnot{B}$\hfill\alert{Differenz} |
| 109 \item[$A \setsymdiff B$] $\defeq \left( A \setminus B \right) \cup \left( B \setminus A \right)$\hfill\alert{Symmetrische Differenz} | 109 \item[$A \setsymdiff B$] $\defeq \left( A \setminus B \right) \cup \left( B \setminus A \right)$\hfill\alert{Symmetrische Differenz} |
| 110 \end{description} | 110 \end{description} |
| 111 \end{block} | 111 \end{block} |
| 112 \vill | 112 \vfill |
| 113 Für mehrere Mengen schreibt man | 113 Für mehrere Mengen schreibt man |
| 114 \begin{align} | 114 \begin{align} |
| 115 \bigcap_{i=1}^n A_i &\defeq A_1 \cap A_2 \cap \ldots \cap A_n\\ | 115 \bigcap_{i=1}^n A_i &\defeq A_1 \cap A_2 \cap \ldots \cap A_n\\ |
| 116 \bigcup_{i=1}^n A_i &\defeq A_1 \cup A_2 \cup \ldots \cup A_n | 116 \bigcup_{i=1}^n A_i &\defeq A_1 \cup A_2 \cup \ldots \cup A_n |
| 117 \end{align} | 117 \end{align} |
| 197 \begin{theorem}[De Morgansche Gesetze] | 197 \begin{theorem}[De Morgansche Gesetze] |
| 198 Sind $A, B$ Mengen, dann gilt | 198 Sind $A, B$ Mengen, dann gilt |
| 199 \begin{alignat}{2} | 199 \begin{alignat}{2} |
| 200 \setnot{A \cup B} &= \setnot{A} \cap \setnot{B} \qquad\qquad& \setnot{A \cap B} &= \setnot{A} \cup \setnot{B}\\ | 200 \setnot{A \cup B} &= \setnot{A} \cap \setnot{B} \qquad\qquad& \setnot{A \cap B} &= \setnot{A} \cup \setnot{B}\\ |
| 201 \intertext{Für Mengen $A_i$ gilt} | 201 \intertext{Für Mengen $A_i$ gilt} |
| 202 \setnot{\bigcup_{i=1}^nA_i} &= \bigcap_{i=1}^n\setnot{A_i} & \setnot{\bigcap_{i=1}^nA_i} &= \bigcup_{i=1}^n\setnot{A_i} & | 202 \setnot{\bigcup_{i=1}^nA_i} &= \bigcap_{i=1}^n\setnot{A_i} & \setnot{\bigcap_{i=1}^nA_i} &= \bigcup_{i=1}^n\setnot{A_i} |
| 203 \end{alignat} | 203 \end{alignat} |
| 204 \end{theorem} | 204 \end{theorem} |
| 205 | 205 |
| 206 \vfill | 206 \vfill |
| 207 | 207 |