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Math Help - show violation of metric definition

  1. #1
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    show violation of metric definition

    Let he function # : PxP->R be defined as
    #((x1,y1),(x2,y2))=((x2-x1)^3+(y2-y1)^3)^(1/3)

    Show that # violates all four conditions that define a metric
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  2. #2
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    Quote Originally Posted by nikie1o2 View Post
    Let he function # : PxP->R be defined as
    #((x1,y1),(x2,y2))=((x2-x1)^3+(y2-y1)^3)^(1/3)

    Show that # violates all four conditions that define a metric
    You really need to learn to use LaTeX!

    Metrics are non-negative. Find points that give a negative value.
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by nikie1o2 View Post
    Let he function # : PxP->R be defined as
    #((x1,y1),(x2,y2))=((x2-x1)^3+(y2-y1)^3)^(1/3)

    Show that # violates all four conditions that define a metric
    For the second condition note that (-1,0)\ne(1,0) but \#((-1,0),(1,0))=0
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