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Home » Sei die Breite \( w \), dann ist die Länge \( 2w \). - Professionaloutdoormedia

Sei die Breite \( w \), dann ist die Länge \( 2w \). - Professionaloutdoormedia

📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 $ y \mid 0 $: $ 0 \mid 0 $: wahr â Implikation wahr.

📌 $ x \mid 0 $: wahr â ganze Aussage wahr.

📌 Also: FÃ¼r **alle** $ x \in \mathbb{Z} $ ist $ x \mid 0 $ wahr, und da $ x \mid y \Rightarrow y \mid x $ fÃ¼r alle $ x \in \mathbb{Z} $ gilt **vergleichsweise begrenzt**, nÃ¤mlich fÃ¼r $ |x| \leq 1 $, und fÃ¼r $ |x| > 1 $ ist $ x \mid y \Rightarrow y \mid x $ falsz â $ P $ falsz â $ P \Rightarrow Q $ wahr.

📌 Aber ist $ x \mid y \Rightarrow y \mid x $ fÃ¼r **alle** $ x, y \in \mathbb{Z} $ wahr?

📌 Nein!** Gegenbeispiel: $ x = 2 $, $ y = 4 $: $ 2 \mid 4 $: wahr, $ 4 \mid 2 $? falsch â Implikation falsz.

📌 Also fÃ¼r $ x = 2 $, $ P $ falsz â $ P \Rightarrow Q $ wahr â Aussage wahr.

📌 Aber ist die gesamte Implikation $ orall x\, (P \Rightarrow Q) $ **echt wahr**?

📌 Nur wenn $ P \Rightarrow Q $ wahr **fÃ¼r alle $ x $**.

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