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Two inequalities help

  1. Aug 22, 2010 #1
    1. The problem statement, all variables and given/known data

    [tex]||a|-|b||\leq{i don't know from here}\leq|a|-|b|\leq|a-b|[/tex]

    2. Relevant equations

    n/a

    3. The attempt at a solution

    help
     
  2. jcsd
  3. Aug 22, 2010 #2

    hunt_mat

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    Homework Helper

    Re: inequality

    You should know that:
    [tex]
    |x+y|\leqslant |x|+|y|
    [/tex]
    So, we can write:
    [tex]
    |x|=|x-y+y|\leqslant |x-y|+|y|
    [/tex]
    Likewise
    [tex]
    |y|=|y-x+x|\leqslant |x-y|+|x|
    [/tex]
    These two inequalities should answer your question.
     
  4. Aug 22, 2010 #3
    Re: inequality

    i knoe, but that would only answer this
    [tex]
    |a|-|b|\leq|a-b|
    [/tex]

    but this one, is it related? i can't see T_T
    [tex]
    ||a|-|b||\leq|a-b|
    [/tex]
     
  5. Aug 22, 2010 #4

    hunt_mat

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    Re: inequality

    it shows that:
    [tex]
    |a|-|b|\leqslant |a-b|
    [/tex]
    and
    [tex]
    -(|a|-|b|)\leqslant |a-b|
    [/tex]
     
  6. Aug 22, 2010 #5

    hunt_mat

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    Re: inequality

    finally the penny drops. This is why I recommended the analysis books!!!
     
  7. Aug 22, 2010 #6
    Re: inequality

    i still, like structure more than limit tough, maybe the reason i dislike analysis NOW(maybe later i love it more) because now i'm studying calculus and some methodS, too much memorizing, not vigorous at all, which despise me. ngahaha
     
  8. Aug 22, 2010 #7

    hunt_mat

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    Homework Helper

    Re: inequality

    Give it time to internalise. Analysis was my first love in maths
     
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