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

  1. Apr 21, 2013 #1
    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. jcsd
  3. Apr 21, 2013 #2

    dx

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    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 ∅ - ∅ = ∅
     
  4. Apr 21, 2013 #3
    Thanks!
     
  5. Apr 22, 2013 #4

    MathematicalPhysicist

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