# 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.

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#### 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.

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