Definition: Isolated Point (Real Numbers)

Let $(x_n)_{n\in\mathbb N}$ be a real sequence $(x_n)_{n\in\mathbb N}$ is said to have an isolated point $a$, if there is an $\epsilon > 0$ and an index $N(\epsilon)$ such that for $|x_n - a| > \epsilon$ for all $n\ge N(\epsilon).$

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