# Math Help - Real Analysis: Limit Points

1. ## 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.

Thanks!

2. How many limit points does $S=\{\frac1n\in\mathbb{R}\mid n\in\mathbb{N}\}$ have? Can you work from there?

3. 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?

4. $\left\{ {1 + \frac{1}
{n}:n \in \mathbb{Z}^ + } \right\} \cup \left\{ {2 + \frac{1}
{n}:n \in \mathbb{Z}^ + } \right\} \cup \left\{ {3 + \frac{1}
{n}:n \in \mathbb{Z}^ + } \right\}$