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I Contradiction in an absolute value property?

  1. Apr 10, 2017 #1
    An absolute value property is
    $$\lvert a \rvert \geq b \iff a\leq-b \quad \text{ or } \quad a\geq b,$$ for ##b>0##.

    Is this true for the case ##a=0##?
    I mean if ##a=0, \lvert a \rvert =0## so ##0 \geq b##. But ##b## is supposed to be ##b>0##, so we have a contradiction.

    How can this property be true if ##a=0## is false?
     
  2. jcsd
  3. Apr 10, 2017 #2

    BvU

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    It's not the property you are 'testing', but the statement . The statement holds.
     
  4. Apr 10, 2017 #3

    mfb

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    Staff: Mentor

    For a=0, b>0, both sides of the equivalence are false. The equivalence itself is correct.
     
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