Set-theoretic limit

In mathematics, the limit of a sequence of sets is a set whose elements are determined by the sequence in either of two equivalent ways:

• Using indicator variables, let equal 1 if x is in A_i and 0 otherwise. If the limit as i goes to infinity of x_i exists for all x'', define

• Using union and intersection, define

and

.

If these two sets are equal, then either gives the set-theoretic limit of the sequence.