Set Theory – Empty Set Does Not Belong to Empty Set

elementary-set-theory

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} $ยท

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

Best Answer

Of course the empty set is not an element of the empty set. Nothing is an element of the empty set. That's what "empty" means.