TITLE: Is $\{\}\;, \{\{\}\}\;\;,\{\{\{\}\}\}$ is an empty set or not?
QUESTION [6 upvotes]: Which of the following sets are equivalent to the empty set?

$\{\}$
$\{\{\}\}$
$\{\{\{\}\}\}$


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.

REPLY [19 votes]: 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?