From 8afd1da9fc39238297c8df3d7568109c8059bab3 Mon Sep 17 00:00:00 2001 From: flavis Date: Wed, 4 Dec 2019 20:38:18 +0100 Subject: [PATCH] update la7 --- lecture.cls | 2 +- ws2019/ipi/uebungen/ipi6.pdf | Bin 73626 -> 73626 bytes ws2019/la/uebungen/la7.pdf | Bin 110439 -> 110481 bytes ws2019/la/uebungen/la7.tex | 16 ++++++++-------- 4 files changed, 9 insertions(+), 9 deletions(-) diff --git a/lecture.cls b/lecture.cls index 9544db7..fe2af32 100644 --- a/lecture.cls +++ b/lecture.cls @@ -48,7 +48,7 @@ \newtheorem{bsp}[satz]{Beispiel} \newtheorem{bem}[satz]{Bemerkung} -\newtheorem{aufgabe}[satz]{Aufgabe} +\newtheorem{aufgabe}{Aufgabe} \newcommand{\N}{\mathbb{N}} \newcommand{\R}{\mathbb{R}} diff --git a/ws2019/ipi/uebungen/ipi6.pdf b/ws2019/ipi/uebungen/ipi6.pdf index 36a980dd9dd20d87eb20582e6e9fd1066b9022bd..f1a8ef9bbfa6f499fe9fd65c046b79def8e1e0a2 100644 GIT binary patch delta 133 zcmbQWpJmp5mWC~i5BN2W42;bU&9w~-)eQ{PHM#VC^HW?BOHvgyT&#=?3@r_f3``(O zwsQ(FuHqrt delta 133 zcmbQWpJmp5mWC~i5BN0=jf@P9Ewv2{)eQ{PHM#VC^HW?BOHvgyT&#=?3@r_f3``(O zwsQ(FuH}gvx~E@zXct|EH=VK7w;n_m==)($-vs^;wpMG`O|Wp%s0t&CZ(J_T`iK!f6YAm z=f!#U`c_JHd9z+@FIV&3&cCN7W;z4IwVwR`13pbQ%PCB@{%NOV+>6 z!1#Z%r)SHbmmgQl>5muRojt!e`{@jjTpq!mJRUO{i|E~_vo}BT=n6mjF5>u>i$13d zKSfI75{r+k=;hg8iVg2ys}QYIe=NqYw?GtHFclv_1|TfNk=2eF+XjM1!Y~jnhd^-O zF&CT2nwSYCGxk5ddB2!nPG`bRk~%|TU=r*YxPfb?lt_`w0y)%Cf)tF8gj3xPk>Qq>nSky+II?! 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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*} w_1(n) + w_1(n+1) + w_1(n+2) &= 1 + 0 - 1 = 0 \intertext{und} w_2(n) + w_2(n+1) + w_2(n+2) &= 0 + 1 - 1 = 0 .\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. Wähle $a_1 := f(1)$ und $a_2 := f(2)$. Damit gilt: