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

1. Apr 21, 2013

### 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?

2. Apr 21, 2013

### 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 ∅ - ∅ = ∅

3. Apr 21, 2013

### talknerdytome

Thanks!

4. Apr 22, 2013

### MathematicalPhysicist

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