Is the empty set disjoint with itself?

  • Thread starter 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]?
 

HallsofIvy

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Yes, it is certainly true that [tex]\oslash\cap\oslash=\oslash[/tex].
 
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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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