Confusion about the boundary of a simple set

1. Aug 31, 2014

Nathanael

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

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

$0<\left| z-z_0 \right|<2$

2. The attempt at a solution

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

Why should the answer not be "... together with the point $z_0$"?

2. Aug 31, 2014

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.

3. Aug 31, 2014

HallsofIvy

Staff Emeritus
Yes, that was clearly a typo.

4. Sep 1, 2014

Nathanael

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.