The statement that the set \(\mathcal{S}=\left\{\dfrac{i}{n}:n\in\mathbb{Z}^+\right\}\) is closed means that \(\mathcal{S}\) contains all of its limit points.
The set \(\mathcal{T}=\left\{{i}\cdot{n}:n\in\mathbb{Z}^+\right\}\) has no limit point so the set is closed.
But because that you do not know what a neighborhood of a point is that is. Thus there no way for you to understand if the set \(\mathcal{S}\) has any limit points.
Is \(\mathcal{S}\) closed or not?
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