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Is this a 'correct' definition?

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Is this a 'correct' definition?

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- Mar 5, 2012

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From wiki:

Is this a 'correct' definition?

A point x in X is a limit point of S if every neighbourhood of x contains at least one point of S different from x itself.

I'm afraid you will need a sequence of points

Btw, I consider this more

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So not every point of a set is limit point? Blast I've been using in a casual way for years. That's completely unintuitive to disbar the constant sequence, what harm can it do?From wiki:

A point x in X is a limit point of S if every neighbourhood of x contains at least one point of S different from x itself.

I'm afraid you will need a sequence of pointsdifferentfrom x.

Btw, I consider this moreTopologythan Analysis, so I am moving it there.

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Correct.So not every point of a set is limit point? Blast I've been using in a casual way for years. That's completely unintuitive to disbar the constant sequence, what harm can it do?

- Jan 26, 2012

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Here is an example.

Is this a 'correct' definition?

Suppose that $X = [0,1]\cup \{2\}$, usual real-line topology.

Every $x$ such that $0\leq x\leq 1$ is a limit point, because we can converge to $x$ along a sequence of points