The discussion revolves around determining the boundary of a set defined by the inequality 0<|z-z0|<2, where z=(x,y). Participants are examining the interpretation of the boundary in relation to the points included in the set.
Some participants express uncertainty about the correctness of the book's answer, suggesting that it may not accurately represent the boundary as defined by the original inequality. There is an acknowledgment of potential typographical errors in the book's solution.
One participant notes that this is their first exposure to these concepts, indicating a learning context where foundational understanding is being developed.
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.Nathanael said:Homework Statement
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]"?
Yes, that was clearly a typo.Nathanael said:Homework Statement
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]"?