This is part of a bigger problem I'm working on.
To construct a a decreasing sequence of sets, $A_{n}\supseteq A_{n+1}$, I did the following: Let $B=\cup_{n=1}^{\infty} B_n$ and set $A_n= B\setminus (B_1\cup\ldots\cup B_n).$ Is this right? Do the B_j's have to be disjoint?
How do I construct the increasing counterpart?
thanks.