# If $\epsilon=\{\}$ then what is $\bigcup \epsilon$ and $\bigcap \epsilon$? [duplicate]

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?

• There are probably more than a handful of other duplicates. Please make sure that you search the site before posting questions. – Asaf Karagila Feb 6 '19 at 10:30

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 ).