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Absolute value proof

  1. Nov 7, 2012 #1
    1. The problem statement, all variables and given/known data
    If a,b,c and are all positive, and if [itex] |a-b| < c-b [/itex], then prove or find a counterexample to [itex] |a|<c [/itex]


    2. Relevant equations



    3. The attempt at a solution
    So far I have been able to show [itex] |a-b|<c [/itex] but don't know what to do next.

    THanks!

    BiP
     
  2. jcsd
  3. Nov 7, 2012 #2

    SammyS

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    You proved that [itex] |a-b|<c \ ?\ \ [/itex] How did you do that?

    Let a = 1, b = 10 and c = 2 .
     
  4. Nov 7, 2012 #3
    Hey Sammy, I think I edited the problem before your post, I don't know how this happened. Please read my edited post again thanks.

    BiP
     
  5. Nov 7, 2012 #4
    I think you are a bit confused. For example, why do you have [itex]|a|[/itex] when you know that [itex]a[/itex] is positive anyway?
     
  6. Nov 7, 2012 #5

    micromass

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    Use

    [tex]a=(a-b)+b[/tex]
     
  7. Nov 7, 2012 #6
    I see! Do you want me to then use the fact that [itex] |a+b| ≤ |a|+|b| [/itex] Thanks micro!

    BiP
     
  8. Nov 7, 2012 #7

    micromass

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    Don't ask, try! :biggrin:
     
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