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How to plot this region in (x,y) space

  1. Nov 19, 2005 #1
    Hi everyone

    I need some help with an elementary problem...I have to sketch the region described by

    [tex]max(|x|,|y|) \leq 1[/itex]

    I know what max and mod (absolute value) mean but I'm just troubled because of the occurence of [itex]|y|[/itex]. Any help would be appreciated...

    PS--This is not homework.

    Thanks and cheers
    Vivek
     
  2. jcsd
  3. Nov 19, 2005 #2
    This is just the desciption of the square of 2unit side length, centered in (0,0). Usually in that kind of formalism, (x,y) are describing the coordinates of a point on a "ideally" flat infinite plane...In your case you just take all points for which -1<=x,y<=1 which is separated into -1<=x<=1 and -1<=y<=1, because there is no relationships between x and y given here.
     
  4. Nov 21, 2005 #3
    Thanks.

    The thing is..how do you reconcile with the occurence of [itex]|y|[/itex]?? I mean....how are you to compare the two operands? Are x and y independent variables in the two orthogonal directions?

    I know that

    [tex]max(x,y) = \frac{x+y}{2} + |\frac{x-y}{2}|[/tex]

    Does this fit in somewhere?
     
  5. Nov 22, 2005 #4
    Yes, x and y are independent...you just compare as the max functions say : max(x,y)=x if x>y and max(x,y)=y if y>x....you could do : max(|x|,|y|)<=1 equiv. to |max(x,y)|<=1 and with your formula : [tex] \frac{1}{2}|x+y+|x-y||<=1[/tex]
     
  6. Nov 26, 2005 #5
    I'm sorry I'm somewhat dumb...I can't see how I can plot the max of two independently varying numbers...some more spoonfeeding needed. :biggrin:
     
  7. Nov 26, 2005 #6

    HallsofIvy

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    If |x|< |y| then max(|x|,|y|)= |y|. Graph |y|= 1.
    If |y|< |x| then max(|x|,|y|)= |x|. Graph |x|= 1.

    Those two graphs form the boundary of the region. Now do you see what the region is?
     
  8. Nov 28, 2005 #7
    Great. Thanks! I see it now :smile:

    I realize how dumb I've been throughout this thread!!!! :cry:

    Anyway thanks for all your help.

    Cheers
    Vivek
     
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