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Does there exist an empty subset of the Cantor set? Or is the empty set, i.e. $\varnothing$, the only empty subset of the Cantor set? http://en.wikipedia.org/wiki/Empty_set

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I don't understand what is being asked. The first sentence of the article you linked to says that the empty set is unique, and your wording implies that you know that it is a subset of the Cantor set. – Jonas Meyer Jul 4 '11 at 20:49

closed as not a real question by Asaf Karagila, t.b., Andres Caicedo, Jonas Meyer, Willie Wong♦ Jul 5 '11 at 12:37

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, see the FAQ.

1 Answer

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As the Wikipedia article says, the empty set, $\emptyset$, is unique: there is only one empty set. It's a subset of every set, empty or not, so it's a subset of the Cantor set, and it's the only empty subset of any set.

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