Would it be correct to say that out of the following two statements, exactly one is always true and one is always false?(adsbygoogle = window.adsbygoogle || []).push({});

1) x is a limit point of S, where S is a subset of ℝ

2) x is an isolated point of S, where S is a subset of ℝ

In other words, every point is either a limit point of a set or an isolated point of that set.

Also, for a point to be a limit point/isolated point of a set, does it have to be in the set?

Thanks!

BiP

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# Limit point and isolated point

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