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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.

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    If you have a decreasing sequence, taking complement usually works for getting an increasing sequence.2012-01-14

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