I am new to this forum so please bear with me if I miss any information. I am currently taking advanced calculus using the textbook Introduction to Analysis ($5$th Ed) by Edward Gaughan. I am having a lot of trouble answering the following question:
Let $S = \left\{n^2 + \left.\frac{1}{k} \right| n, k\ \text{are natural numbers}\right\}$. Find the accumulation points of $S$.
I think I am struggling with just starting how to answer this question.I understand an accumulation point of a set in a topological space is a point that can be “approximated” by other points of the set. More formally, a point $x$ is an accumulation point of a set $S$ if every neighborhood of $x$ contains at least one point of $S$ different from $x$ itself. How do I apply this principle to this type of proof?