- #1
cocobaby
- 9
- 0
Does any subset of natural number N have a cluster point?
And does it diverge?
And does it diverge?
A cluster point, also known as a limit point, is a point in a topological space that has a set of points within a certain distance from it.
Although they are often used interchangeably, a cluster point and a limit point have subtle differences. A cluster point must have a set of points within a certain distance, while a limit point must have an infinite number of points within a certain distance.
Cluster points play a crucial role in the study of topology and analysis. They help us understand the behavior of sequences and the convergence of functions.
To determine if a point is a cluster point, you must check if there is a sequence of points within a certain distance from the point. If there is, then the point is a cluster point.
Yes, a point can be both a cluster point and a limit point. However, not all cluster points are limit points and vice versa.