Why is the empty set not a subset of the set of an empty set?

Question

Im wondering, because several sources state that the empty set is a subset of EVERY set. Yet this instance seem to be proving that statement wrong. 

 

Update: To be more specific and clear, the following statement is WRONG, but i dont fully understand why.

 

• Ø ⊆ {Ø}

 

However, all of the statements shown under here are true, which have the same kind of structure except the set does not have the empty set as an element:

 

• Ø ⊆ {1}
• Ø ⊆ {0,3,3,1,2,9}
• Ø ⊆ ℤ

 

Answer 1

I think that ∅⊆{Ø} is considered false because Ø is an element of {∅}, and not a subset.

If you had ∅∈{∅}, then this would be true.

If you had ∅⊆{1,2,3}, then this would be true because you don't actually have the symbol "∅" as an element of the set.

This leads to the question: How to show that the empty set is a subset of {∅}.

If you had { }⊆{∅}, then this would be considered true.

Answer 2

Please show the problem that claims this is wrong.

 

Every set is a subset of itself by reflexive property.

 

Since the empty set contains no elements, it is a subset of itself.