Explore BrainMass

Explore BrainMass

    Cluster point proof

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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

    Solution Preview

    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 ...

    Solution Summary

    This provides an example of proving there are no cluster points in a set.