Hi, may be you can choose to see them separately and therefore imply that the infinite sets actually are composed of both increasing and decreasing series. Then both signs are indeed logical.
hi.. i have no idea what the question is asking...specifically two unions and intersections. how is it possible that 2 of them are used joined together?
is it possible for someone to give some pointers? thanks.
Reading stuff about Borel-Cantelli's lemma may enlighten your problem.
The first one is "logic". Maybe Laurent will better be your man to explain it lol.
The second one is exactly the lemma. So you're asked to prove it. There are various way to prove that, google for it.