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    Cluster point proof

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    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
    https://brainmass.com/math/real-analysis/cluster-point-proof-220708

    Solution Preview

    In this problem, we need to use the following theorem:
    Any infinite bounded set must have a cluster point.

    Proof:
    "=>": 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.

    $2.49

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