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Which of the following sets are equivalent to the empty set?

  1. $\{\}$
  2. $\{\{\}\}$
  3. $\{\{\{\}\}\}$

My Opinion: The first is the empty set because it contains no elements. The second and third sets are not the empty set because each contains an empty set.

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  • $\begingroup$ Can you define each of them? Remember that $\{ \varnothing \} \ne \varnothing$. Also, $\varnothing \notin \{ \{ \varnothing \} \}$ (you mentioned that the third set contains the empty set) $\endgroup$ – A.S Apr 22 '13 at 5:46
  • $\begingroup$ If by double brackets you mean $\{ \} = \emptyset$, then you're correct. The second two are not empty and the first one is. $\endgroup$ – Suugaku Apr 22 '13 at 5:47
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Yes. The first set is the only empty set. To convince yourself that the other two are not empty sets, try to answer these two questions:

$1$. Is a bag containing an empty bag empty?

$2$. Is a bag containing a bag, that contains an empty bag, empty?

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