Q: Find a sequence having only one cluster point, yet not convergent.
Solution:
Let N = 1,2,1,3,1,4,1,5,....,1,n,.....
Clearly 1 is a cluster points of N, yet N is unbounded.
Just wondering if this solution is correct? Any suggestions!!!
Thanx
For a sequence be say that is an accumulation point if for any there exists a distinct so that . In your example is not an accumulation point because if the only terms of the sequence that are within to is just itself. It needs to be distinct from .