Can we say that $\emptyset\in\{\emptyset\}$?

Question

Is it correct to say that $\emptyset\in\{\emptyset\}$? By definition, the empty set does not contain anything so how can we say that empty belongs to the empty set. And also whether it is right to say that the empty set is contained in empty? I am really confused about this. Please help.

Answer 1

$\{\emptyset\}\neq\emptyset$

$\{\emptyset\}$ is a set consisting of one element. That one element is the empty set.

Answer 2

Yes. It is the only one element of the set $\{\emptyset\}$

Answer 3

"$\{\varnothing\}$" is not "the empty set"; it is "the set containing the empty set".

• $\varnothing$: the empty set
• $\{\}$: the empty set
• $\{\text{Earth}\}$: the set containing "Earth"
• $\{ \varnothing \}$: the set containing the empty set
• $\{ \{\} \}$: the set containing the empty set