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Homework Statement
Prove that if [itex]E \subset X[/itex] and if p is a limit point of E, then there is a sequence [itex]\{p_{n}\}[/itex] in [itex]E[/itex] such that [itex]p=\lim_{n\to\infty}\{p_{n}\}[/itex] (I presume that there is an invisible "[itex]p_{n} \rightarrow p[/itex] implies that" at the beginning of the sentence).
Homework Equations

The Attempt at a Solution
We want to show that every neighbourhood around p contains infinitely many [itex]p_{n}[/itex]'s.
By the definition of convergence we can choose infinitely many N's so that infinitely many [itex]p_{n}[/itex]'s can be contained in a neighbourhood of p with a correspondent radius.
Is this valid?