(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find a sequence whose set of subsequential limits is the interval [0,1].

2. Relevant equations

If the sequence does not repeat itself, then any subsequential limit is a cluster point.

3. The attempt at a solution

I've an idea that [itex]|\sin n|[/itex] is a solution to this, but I'm not sure how to prove this.

What I need to show is that, since the sequence I've chosen is non-repeating, then every point in the interval [0,1] is a cluster point. That is, if I take any number in [0,1] and am given an epsilon>0, can I always find an infinite amount of members in the sequence in an epsilon neighborhood around the number? This seems to intuitively work since [itex]|\sin n| [/itex] is all over the interval [0,1] (though not necessarily touching every point in the interval), but can this argument be made more rigorous? Any suggestions?

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# Homework Help: Cluster Points

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