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Inequality with absolute values

  1. May 7, 2014 #1
    Wonder if this is true or just mistype:

    |x+y| [itex]\leq[/itex] |x| +|y|

    If this is true how to proof because cannot find it out anywhere written
  2. jcsd
  3. May 7, 2014 #2


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    Gold Member

    wouldn't it be easy to demonstrate this by putting in numbers?
  4. May 7, 2014 #3


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    Science Advisor

    What have you tried?
  5. May 7, 2014 #4
    Yes, please tell us what you tried.

    Did you try plugging in some random numbers to check whether it works?
    If it does always work, did you attempt a proof?
  6. May 7, 2014 #5


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    Science Advisor

    There are basically two cases - x and y same sign, x and y opposite sign. Work out each case.
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