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Home » The highest power of 2 is \( 2^3 \). - Get link 4share

The highest power of 2 is \( 2^3 \). - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 FÃ¼r $ x = 0 $: Jedes $ y $ ist durch $ 0 $ teilbar ($ 0 \mid y $) nur wenn $ y = 0 $, da $ 0

📌 mid y $ fÃ¼r $ y

📌 e 0 $. Also $ 0 \mid y $ ist falsz, so dass die Implikation $ 0 \mid y \Rightarrow y \mid 0 $ hier irrelevant ist (PrÃ¤misse ist leer wahr oder nur fÃ¼r $ y=0 $). TatsÃ¤chlich gilt:

📌 FÃ¼r $ x = 0 $, die Implikation $ (orall y\ (0 \mid y \Rightarrow y \mid 0)) $ ist *wahr*, denn der Antezedens ist nur fÃ¼r $ y = 0 $ wahr, und $ 0 \mid 0 $ ist wahr.

📌 Aber $ 0 \mid 0 $ ist wahr â also ist die Implikation wirklich **wahr** fÃ¼r $ x = 0 $.

📌 FÃ¼r $ x = 1 $: $ x \mid y \iff y = k \cdot 1 = k $, also $ y $ ist beliebig teilbar â $ y \mid x $? $ y \mid 1 $ â $ y = \pm1 $. Also $ x \mid y \Rightarrow y = \pm1 $, aber $ (\pm1) \mid 1 $: wahr. Also **ja**, $ x \mid y \Rightarrow y \mid x $ gilt.

📌 Und $ x = 1 $, $ 1 \mid 0 $: wahr. Also Aussage gilt.

📌 FÃ¼r $ x = -1 $: gleiche Logik wie bei $ x = 1 $, da Teiler keine Vorzeichen betreffen.

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