Is the empty set disjoint with itself?

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SUMMARY

The empty set is disjoint with itself, as established in set theory. The intersection of the empty set with itself is represented as ∅ ∩ ∅ = ∅, confirming that there are no elements in common. Disjoint sets are defined as sets that do not share any elements, and since the empty set contains no elements, it cannot share any with itself. Therefore, the claim that the empty set is not disjoint from itself is incorrect.

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CantorSet
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My apologies if the following is a stupid question. But is the empty set disjoint with itself? Certain aspects of set theory has always been counter-intuitive for me.

[tex]\oslash\cap\oslash=\oslash[/tex]?
 
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Yes, it is certainly true that [tex]\oslash\cap\oslash=\oslash[/tex].
 
If A and B are not disjoint, it means there is some element belonging to both of them. Anyone who claims the empty set is not disjoint from itself must provide us with an element belonging to the empty set!
 

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