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Help me to show this inequality ?

  1. Nov 8, 2008 #1
    Help me to show this inequality ????


    I have to show this inequality

    | ||x||-||y|| | <= ||x-y||

    I have tried to use the Couchy-Schwarz inequality but I didn't get anything.

    Could anyone help me solving this.

    Thanks a lot.

  2. jcsd
  3. Nov 8, 2008 #2


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    Staff Emeritus
    Science Advisor

    Re: Help me to show this inequality ????

    The Cauchy-Schwarz inequality says that [itex]||x+ y||\le ||x||+ ||y||[/itex].

    If you let x= a-b and y= b, that becomes [itex]||a-b+b||\le ||a- b||+ ||b||[/itex] or [itex]||a||\le ||a- b|+ ||b||[/itex] which, subtracting [itex]||b||[/itex] from both sides, gives [itex]||a||- ||b||\le ||a- b||[/itex]. You Should be able to use that.
  4. Nov 8, 2008 #3
    Re: Help me to show this inequality ????

    Thanks a lot
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