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for all $ a, b, c \in \mathbbR $. - Londonproperty

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Somit ist die **PrÃ¤misse fÃ¼r $ x = 5 $ falsz**, also die gesamte Implikation: â(PrÃ¤misse â $ x \mid 0 $)â â falsch â beliebig â **gesillt falsz**.

📌 Aber ist die PrÃ¤misse *immer* falsz?

📌 TatsÃ¤chlich gilt:

📌 Die Aussage $ orall y\ (x \mid y \Rightarrow y \mid x) $ ist **nur wahr**, wenn $ x $ ein **lattice complÃ¨te teiler** ist â d.h., wenn $ x $ *positiv* oder $ x = 0 $ ist, und besonders, wenn $ x = \pm1, 0 $, aber fÃ¼r $ |x| > 1 $:

📌 Nehmen wir $ y = x^2 $: $ x \mid y $: wahr. $ y \mid x $? $ x^2 \mid x $ â $ x \mid 1 $ â $ |x| = 1 $.

📌 Donutalo: Die Bedingung $ x \mid y \Rightarrow y \mid x $ ist **nur wahr, wenn $ x = 0 $ oder $ |x| = 1 $**.

📌 FÃ¼r $ x = 0 $: $ x \mid y $ nur wenn $ y = 0 $. Dann $ y \mid x $? $ 0 \mid 0 $: wahr. Also PrÃ¤misse wahr. $ x \mid 0 $? wahr â Implikation wahr.

📌 FÃ¼r $ x = 1 $: $ x \mid y \Rightarrow y \mid 1 $ â $ y = \pm1 $, aber $ y \mid 1 $: nur $ y = \pm1 $. $ y \mid x $? $ \pm1 \mid 1 $: wahr â Implikation wahr. $ x \mid 0 $? wahr â Implikation wahr.

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