What is the interpretation of ∅-∅?

[Aziza]

What is ∅-∅ equal to?
Logically this is represented as the set containing all x such that x\in∅ and x\notin∅. I am confused on how to interpret this...I think the answer would just be the null set, but I am not sure. Could someone please clarify this?

 

[happysauce]

Think of the subtraction of sets as the intersection of the one with the complement of the other. That is ∅\cap ∅^{c}

 

[vela]

There is no $x$ for which $x \in \emptyset$ and $x \notin \emptyset$, so there are no elements in $\emptyset - \emptyset$.

 

[Mark44]

Makes me think of the song quite a few years back, "Nothin' from nothin' leaves nothin." - Billy Preston, 1975

 

[SammyS]

Makes me think of the song quite a few years back, "Nothin' from nothin' leaves nothin." - Billy Preston, 1975

Great post, Mark !

 

[Mark44]

Great post, Mark !

 

[Hurkyl]

What is ∅-∅ equal to?
Logically this is represented as the set containing all x such that x\in∅ and x\notin∅. I am confused on how to interpret this...I think the answer would just be the null set, but I am not sure. Could someone please clarify this?

That is exactly right. It may help to simplify that logical expression, because you can, for example, replace x \in \emptyset with a truth value.

Or maybe slightly reorganizing it to the fact that

x is in ∅-∅​

is synonymous with

x\in∅ and x\notin∅​