Union and Intersection of empty class of sets

  • #1

Main Question or Discussion Point

why intersection of empty class of sets is the whole space while their union is null set?
Book writes that an element will fail to be in the intersection if it fails to be in one of the sets of the class but since there is nothing in the empty class so there is nothing in the empty class that contradicts that an element does not belong to the intersection so in this way intersection is the whole space. ASSUME THIS IS TRUE. Then why don't they use the same arguments for the union? Then union should also have been the whole space......
 

Answers and Replies

  • #2
mathman
Science Advisor
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The argument for the union is similar. To be in the union an element has to be in at least one of the sets. Since all the sets are empty, the union is empty.
 

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