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]"?
A simple set is a collection of distinct objects or elements that can be easily defined and counted. It is a fundamental concept in mathematics and is often used to model real-world scenarios.
The boundary of a simple set is the set of points that lie on the edge of the set. It includes both the elements of the set and the elements that are not part of the set but are adjacent to it.
The boundary of a simple set can be calculated by taking the closure of the set (the set of all points that are either part of the set or are limit points of the set) and then subtracting the interior of the set (the set of all points that are contained within the set).
There is confusion about the boundary of a simple set because it is a concept that is often misunderstood or misinterpreted. Additionally, the boundary can be different depending on the topology used to define the set, leading to different interpretations.
The boundary of a simple set is commonly used in scientific research to define and analyze data sets. It can also be used to model and understand complex systems and their interactions with their environments.