TITLE: Empty set does not belong to empty set
QUESTION [13 upvotes]: Herbert in his book "Elements of set theory" on page no 3 says that 

we can form the set $ \{ \emptyset \} $ whose only member is $\emptyset $. Note that $ \{ \emptyset \} \neq  \emptyset $, because $ \emptyset \in \{ \emptyset \} $ but $\underline{ \emptyset \notin \emptyset} $·

By the last argument $\emptyset \notin \emptyset$, is he saying that empty set is not a member of or does not belong to empty set
OR
it is a typo and he wanted it to be $ \{\emptyset \} \notin \emptyset $, that set containing empty set is not a member of empty set

REPLY [4 votes]: The general form of the argument he makes is

$A\ne B$ because $C\in A$ but $C\notin B$.

That, by definition, is how you prove that two sets are different from each other -- you prove that there is something that is member of one but not of the other.
What you're reading is simply this argument where $A$ is $\{\varnothing\}$, and $B$ and $C$ both happen to be $\varnothing$.