# 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?

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#### dx

Homework Helper
Gold Member
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 ∅ - ∅ = ∅

Thanks!

#### MathematicalPhysicist

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

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