I know that $\bigcup \epsilon$ is the union of sets that are members of collection set $\epsilon$, and $\bigcap \epsilon$ is the intersection of sets that are members of collection set $\epsilon$. But what if the set (for this question is $\epsilon$) is an empty collection of sets, what would the union and intersection be?
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There are probably more than a handful of other duplicates. Please make sure that you search the site before posting questions. – Asaf Karagila Feb 06 '19 at 10:30
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If $\epsilon = \emptyset $, then of course $\bigcup \epsilon = \emptyset$, as it a set of elements of elements of $\epsilon$, and since there are no elements of $\epsilon$, there are no elements of $\bigcup\epsilon$. Now for the $\bigcap\epsilon$, this one is actually undefined, as condition of being an element of each element of $\epsilon$ is an empty condition, as there are no elements of $\epsilon$, so everything satisfies it ( if it was defined, it would have been a set of everything, but there is no such a set ).
