---
tag: KWE1DBMN9B
kind: concept
name: Ring of sets
msc: [28A05]
specializes: [PYH82FMXQ2]
sources:
  - url: https://en.wikipedia.org/wiki/Ring_of_sets
same_as:
  wikidata: Q2064647
  wikipedia: Ring of sets
---

## Summary

A ring of sets is a nonempty family of sets that is closed under unions and differences of two members.
It is then closed under intersections and symmetric differences too.
Rings of sets are a common domain for contents and premeasures before they are extended to measures.

## Explanations

### L1 human

A ring of sets is a family of sets in which one can glue two members together and cut one member out of another.
Unlike an algebra of sets, it need not contain a largest set.
For example, the finite subsets of the natural numbers form a ring: the union and the difference of two finite sets are finite.
The name comes from algebra: with symmetric difference as addition and intersection as multiplication, the family is a ring.