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

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    Difference Empty Set
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Discussion Overview

The discussion revolves around the mathematical operation of set difference, specifically focusing on the difference between the empty set and itself. Participants explore the implications of this operation within set theory.

Discussion Character

  • Conceptual clarification, Technical explanation

Main Points Raised

  • One participant expresses difficulty in understanding the difference between the empty set and itself, suggesting that it should return ∅ due to the absence of elements.
  • Another participant explains that subtracting a set A from a set B results in the set obtained by removing elements of A from B, supporting the idea that ∅ - ∅ = ∅.
  • A further comment notes that the difference of the empty set and any nonempty set A also results in the empty set, stated as ∅ - A = ∅.

Areas of Agreement / Disagreement

Participants appear to agree that ∅ - ∅ = ∅, but the discussion does not explore any competing views or deeper implications of this operation.

Contextual Notes

The discussion does not address potential nuances in definitions of set difference or implications for broader set theory concepts.

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

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