Does ∅-∅=∅ or does ∅-∅=0? Difference of the empty set and itself?

[talknerdytome]

I'm having trouble conceptualizing taking the difference between the empty set and itself. There is no element x where x∈∅ and x∉∅, so I'm thinking that it should return ∅ since there are no possible elements.

Is that correct?

 

[dx]

Subtracting a set A from a set B simply means the set that you get if you remove the elements in A from B. So yes ∅ - ∅ = ∅

 

[talknerdytome]

Thanks!

 

[MathematicalPhysicist]

BTW, also $$\emptyset - A =\emptyset$$ where A is nonempty.