I think I'm not understanding something here:(adsbygoogle = window.adsbygoogle || []).push({});

A point [itex]L \in \mathbb{R}[/itex] is a limit point of a sequence [itex] a_n[/itex] if exists a subsequence [itex]b_n[/itex] such that [itex]\lim b_n = L[/itex]

So for example the constant sequence [itex]a_n = 1[/itex] so that [itex]a = 1, 1, 1, 1, 1, 1, \ldots [/itex] has a unique limit point [itex]L=1[/itex]

But a limit point (or acumulation point) is one that can be approached by nearby point in the set. (For example in the open interval [itex](0,2)[/itex] we have that 2 is al limit point, but in the set [itex]S=\{ 1 \}[/itex] we have no limit point (1 is an isolated point in [itex] \mathbb{R}[/itex])

Aren't both definitions of limit point contradictory? What am I doing wrong?

Thanks

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# Limit point of sequence

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