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update la7

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christian
2019-12-04 20:38:18 +01:00
parent a5c210aa6f
commit 8afd1da9fc
4 changed files with 9 additions and 9 deletions
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lecture.cls
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@@ -48,7 +48,7 @@
\newtheorem{bsp}[satz]{Beispiel} \newtheorem{bsp}[satz]{Beispiel}
\newtheorem{bem}[satz]{Bemerkung} \newtheorem{bem}[satz]{Bemerkung}
\newtheorem{aufgabe}[satz]{Aufgabe} \newtheorem{aufgabe}{Aufgabe}
\newcommand{\N}{\mathbb{N}} \newcommand{\N}{\mathbb{N}}
\newcommand{\R}{\mathbb{R}} \newcommand{\R}{\mathbb{R}}
ws2019/ipi/uebungen/ipi6.pdf
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ws2019/la/uebungen/la7.pdf
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ws2019/la/uebungen/la7.tex
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@@ -46,27 +46,27 @@
Definiere: Definiere:
\begin{align*} \begin{align*}
&w_1 := \begin{cases} &w_1 := \begin{cases}
1 & \exists k \in \N\colon n = 3k+1 \\ 1 & \exists k \in \N_0\colon n = 3k+1 \\
0 & \exists k \in \N\colon n = 3k+2 \\ 0 & \exists k \in \N_0\colon n = 3k+2 \\
-1 & \exists k \in \N\colon n = 3k -1 & \exists k \in \N_0\colon n = 3k
\end{cases}, \qquad \end{cases}, \qquad
w_2 \colon= \begin{cases} w_2 \colon= \begin{cases}
0 & \exists k \in \N\colon n = 3k+1 \\ 0 & \exists k \in \N_0\colon n = 3k+1 \\
1 & \exists k \in \N\colon n = 3k+2 \\ 1 & \exists k \in \N_0\colon n = 3k+2 \\
-1 & \exists k \in \N\colon n = 3k -1 & \exists k \in \N_0\colon n = 3k
\end{cases} \end{cases}
.\end{align*} .\end{align*}
Zz.: $w_1, w_2 \in W$. Sei $n \in \N$ beliebig. Zz.: $w_1, w_2 \in W$. Sei $n \in \N$ beliebig.
Falls $\exists k \in \N\colon n = 3k+1$, dann $n + 1 = 3k+2$ und $n + 2 = 3(k+1)$. Falls $\exists k \in \N_0\colon n = 3k+1$, dann $n + 1 = 3k+2$ und $n + 2 = 3(k+1)$.
\begin{align*} \begin{align*}
w_1(n) + w_1(n+1) + w_1(n+2) &= 1 + 0 - 1 = 0 w_1(n) + w_1(n+1) + w_1(n+2) &= 1 + 0 - 1 = 0
\intertext{und} \intertext{und}
w_2(n) + w_2(n+1) + w_2(n+2) &= 0 + 1 - 1 = 0 w_2(n) + w_2(n+1) + w_2(n+2) &= 0 + 1 - 1 = 0
.\end{align*} .\end{align*}
Fälle $\exists k \in \N\colon n = 3k+2$ bzw. $n = 3k$ folgen analog. Fälle $\exists k \in \N_0\colon n = 3k+2$ bzw. $n = 3k$ folgen analog.
Zz.: $\{w_1, w_2\} $ ist Erzeugendensystem. Sei $f \in W$ beliebig. Zz.: $\{w_1, w_2\} $ ist Erzeugendensystem. Sei $f \in W$ beliebig.
Wähle $a_1 := f(1)$ und $a_2 := f(2)$. Damit gilt: Wähle $a_1 := f(1)$ und $a_2 := f(2)$. Damit gilt: