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Unit n - box notation

  1. Sep 16, 2008 #1
    1. The problem statement, all variables and given/known data
    can someone please explan what the line segment [-1,0]x{0} means? i don't understand the notation. if someone could explain it to me it would help me a lot!!

    thanks!


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 16, 2008 #2

    Dick

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    It means the set of all ordered pairs (x,0) where -1<=x<=0.
     
  4. Sep 16, 2008 #3
    so what would [1,0]x[1,0] mean?

    the set of (x,y) such that 1<=x<=0 and 1<=y<=0?

    does the x in between the two [1,0]'s mean anything?
     
  5. Sep 16, 2008 #4

    Dick

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    Sure. If you interpret (x,y) as a point in the plane that's a square. The 'x' is called the cartesian product. AxB is the set of all (x,y) such that x is in A and y is in B. (BTW you usually want to write the unit interval as [0,1], not [1,0]).
     
  6. Sep 16, 2008 #5
    how about in this case?

    S = {(x,y) : x and y are rational numbers in [0,1]}
    the closure and boundary of S = [0,1]x[0,1]

    what would it mean in this case, word for word?
     
  7. Sep 16, 2008 #6

    Dick

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    You know what the sets mean, right? It says that the closure and boundary of the set of all rational points in the filled unit square are equal to ALL points in the filled unit square. (By filled I mean it includes the interior of the square).
     
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