---
tag: 34PGCR9YS6
kind: concept
name: Set-theoretic limit
sources:
  - wikipedia: en:343663@r1304676612
    locator: Set-theoretic limit
    note: adopted
    mention: wikipedia://en/343663
    sections: [Summary]
same_as:
  wikidata: Q1131116
  wikipedia: Set-theoretic limit
inventory: [R5EJB15P13]
---

## Summary

In mathematics, the **limit** of a [[sequence|0G9EKM0E15]] of [[sets|0BSJ7RQ9BW]] $A_1, A_2, \ldots$ ([[subsets|0BJR9QR08E]] 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|05M5SWSZZD]]) and **(2)** by convergence of a sequence of indicator functions which are themselves [[real|08J2M1JYAG]]-valued. As is the case with sequences of other objects, convergence is not necessary or even usual.