Confusion about the boundary of a simple set

[Nathanael]

Homework Statement

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 $z_0$"?

 

[Mark44]

Homework Statement

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 $z_0$"?

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.

 

[HallsofIvy]

Homework Statement

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 $z_0$"?

Yes, that was clearly a typo.

 

[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.