Give an example of a set that has the set of natural numbers as it s set of accumulation points.

Question

So far, I have:

Let $S_k = \{ K + \frac{1}{n}: n \in N \} \ \forall K$.

Example: $S_0 =\{ \frac{1}{n} : n \in N \} $ where there is only one accumlation point.

Are there other examples that of a set that has the set of natural numbers as the set of accumulation points?

Answer 1

Yes:$$\left\{m+\frac1n\,\middle|\,m,n\in\mathbb{N}\right\}.$$