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Consider the following two statements. (Assume $E \subseteq K$.)

$E$ has a limit point in $K$.


$E$ contains a limit point of $K$.

What do they each mean and how are they different?

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English.SE might be a better fit for this question. – Ink Apr 12 '14 at 20:39
@Veckt Funny, but I'm a native speaker and I don't think that the people at English.SE would have the mathematical background to elucidate the difference between them. – AmadeusDrZaius Apr 13 '14 at 9:56
up vote 7 down vote accepted

The first says that there exists an $x\in K$ such that $x$ is a limit point of $E$, whereas the second says that there is a limit point $x$ of $K$ that lies within $E$.

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Thanks to both of you for your answers. They each helped me equally, so I'm choosing Hayden's since (s)he has less points and it was given first. – AmadeusDrZaius Apr 12 '14 at 20:18

The first one means that there is a limit point of $E$, say $x$, where $x\in K$.

The second one means that there is a limit point of $K$, say $y$, where $y\in E$.

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