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Math Help - Real Analysis: Limit Points

  1. #1
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    Real Analysis: Limit Points

    Q: Find a set with exactly three limit points.

    I know it's got to be a set of isolated points that approaches 3 points but I can't think of such a set.

    Help please!!
    Thanks!
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  2. #2
    Senior Member Tinyboss's Avatar
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    How many limit points does S=\{\frac1n\in\mathbb{R}\mid n\in\mathbb{N}\} have? Can you work from there?
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  3. #3
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    so can that set be a union of 3 sets?

    like

    {1/n in R|n in N} U { 1+(1/n) in R| n in N} U {2+(1/n) in R| n in N}

    so I get 3 limit points, 0, 1, and 2?
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  4. #4
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    \left\{ {1 + \frac{1}<br />
{n}:n \in \mathbb{Z}^ +  } \right\} \cup \left\{ {2 + \frac{1}<br />
{n}:n \in \mathbb{Z}^ +  } \right\} \cup \left\{ {3 + \frac{1}<br />
{n}:n \in \mathbb{Z}^ +  } \right\}
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