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Confusion about the boundary of a simple set

  1. Aug 31, 2014 #1

    Nathanael

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    Homework Helper

    1. The problem statement, all variables and given/known data

    Determine the boundary of the following set. As usual, z=(x,y).

    [itex]0<\left| z-z_0 \right|<2[/itex]

    2. The attempt at a solution

    The book's solution says "The circle [itex]\left| z-z_0 \right|=2[/itex] together with the point (0,0)"

    Why should the answer not be "... together with the point [itex]z_0[/itex]"?
     
  2. jcsd
  3. Aug 31, 2014 #2

    Mark44

    Staff: Mentor

    The book's answer seems incorrect to me. The original inequality represents all of the points inside (but not on) the circle of radius 2 with center at z0, not including this center point.
     
  4. Aug 31, 2014 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes, that was clearly a typo.
     
  5. Sep 1, 2014 #4

    Nathanael

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    Thank you both, it's my first time learning these ideas (even if they are fairly simple) so I just wanted to make sure I wasn't misunderstanding.
     
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