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Strict linear order

  1. Dec 5, 2007 #1
    1. The problem statement, all variables and given/known data
    Define a relation on the plane by setting (x_0, y_0) < (x_1, y_1) if either

    [tex] y_0 - x_0^2 < y_1 - x_1^2[/tex], or [tex] y_0 - x_0^2 = y_1 - x_1^2[/tex] and [tex]x_0 < x_1[/tex]

    I showed that this is a strict linear order on the plane but then the question asks me to describe it geometrically. I am not really sure how you describe something like this geometrically. Anyone want to clarify what that means?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Dec 6, 2007 #2


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    Homework Helper

    Try drawing some parabolas!
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