Reelle Zahlen/Betragseigenschaften/Fakt/Beweis/Aufgabe/en

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Prove the following properties for the absolute value function

(here let be arbitrary real numbers).
  1. .
  2. if and only if .
  3. if and only if or .
  4. .
  5. .
  6. For we have .
  7. We have (Triangle inequality for the absolute value).