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Math Help - Absolute values / summation proof

  1. #1
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    Absolute values / summation proof

    hi there,

    I have trouble getting started with proving that:

    abs ( sum over all a ) <= sum over all abs ( a )

    any suggestions (induction proof) would be very welcome.

    thank you -
    oz.
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  2. #2
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    Quote Originally Posted by ozfingwe View Post
    hi there,

    I have trouble getting started with proving that:

    abs ( sum over all a ) <= sum over all abs ( a )

    any suggestions (induction proof) would be very welcome.

    thank you -
    oz.

    Exactly: induction (provided "over all a" means "over all the possible finite values some variable/parameter a can attain").

    Tonio
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  3. #3
    Super Member redsoxfan325's Avatar
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    Swampscott, MA
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    Quote Originally Posted by ozfingwe View Post
    hi there,

    I have trouble getting started with proving that:

    abs ( sum over all a ) <= sum over all abs ( a )

    any suggestions (induction proof) would be very welcome.

    thank you -
    oz.
    This is just the triangle inequality.
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