Prove that a set S included R has no cluster points if and only if S intersection [-n,n] is a finite set for each n in N.© BrainMass Inc. brainmass.com December 15, 2022, 7:26 pm ad1c9bdddf
In this problem, we need to use the following theorem:
Any infinite bounded set must have a cluster point.
"=>": If S has no cluster point, I want to show that S intersection [-n, n] is a finite set for each n in N.
If not, we can find some n in N, such that S intersection [-n, n] is ...
This provides an example of proving there are no cluster points in a set.