Set-theoretic limit

Summary

In mathematics, the limit of a sequence of sets $A_1, A_2, \ldots$ (subsets of a common set $X$) is a set whose elements are determined by the sequence in either of two equivalent ways: (1) by upper and lower bounds on the sequence that converge monotonically to the same set (analogous to convergence of real-valued sequences) and (2) by convergence of a sequence of indicator functions which are themselves real-valued. As is the case with sequences of other objects, convergence is not necessary or even usual.