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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How many limit points does $\displaystyle S=\{\frac1n\in\mathbb{R}\mid n\in\mathbb{N}\}$ have? Can you work from there?
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?
$\displaystyle \left\{ {1 + \frac{1} {n}:n \in \mathbb{Z}^ + } \right\} \cup \left\{ {2 + \frac{1} {n}:n \in \mathbb{Z}^ + } \right\} \cup \left\{ {3 + \frac{1} {n}:n \in \mathbb{Z}^ + } \right\}$
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