4
$\begingroup$

I need to show that if $U$ is a free ultrafilter on $\mathbb N$, then

($A \in U$ and $F \subseteq \mathbb N$ finite) $\implies (A\Delta F) \in U$.

To show this do you need maximality? (Would the same hold for any non-principal/free filter; one such that the intersection of all its sets is empty?)

2 Answers 2