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Proper notation for writing all points in the 1st and 3rd cartesian quadrant?

  1. Aug 28, 2009 #1
    1. The problem statement, all variables and given/known data

    What is the proper notation for writing the set of all ordered pairs of real numbers that are in quadrant 1 and 3 of the real plane?

    2. Relevant equations



    3. The attempt at a solution

    I was thinking something like

    [tex]$\left\{ \left(x_{1},x_{2}\right)\in\mathbb{R}\,:\, x_{1},x_{2}\geq0\right\} +\left\{ \left(x_{1},x_{2}\right)\in\mathbb{R}\,:\, x_{1},x_{2}\leq0\right\} $[/tex]

    Is this fine or will including the + operation mean I am including points in the 2nd and 4th quadrant?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 28, 2009 #2

    Mark44

    Staff: Mentor

    Since you're working with sets, you would want "union" rather than "plus."
     
  4. Aug 29, 2009 #3
    Note: points in quadrants are not on axes and vice-versa, so you need to be careful with the use of >= and >.

    It is also possible to describe the 1st and 3rd quadrants as

    [tex]\{(x,y) \in \mathbb{R}^2:xy<0\}[/tex]

    If you wish to include the axes, change the inequality to xy <= 0.

    --Elucidus
     
  5. Aug 29, 2009 #4
    Thanks for the quick replies.
     
  6. Aug 29, 2009 #5
    ERROR!!

    1st and 3rd should be xy > 0. The coordinates must be of the same sign.

    Sorry, somehow I was thinking 2nd and 4th (sheesh, I feel silly).

    --Elucidus
     
  7. Aug 29, 2009 #6
    No worries I figured it was a typo :)

    Thank you for your time.
     
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