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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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References
Bibliography
 Kane, Jonathan: "Writing Proofs in Analysis", Springer, 2016