---
tag: 1EZAT5BEVJ
kind: concept
name: Cofiniteness
aliases: [co-finite, co-finitely, co-finiteness, co-finitude, cofinite, cofinite-set, cofinite-subset, cofinitely, cofinitely-many, cofinitude, double-pointed-finite-complement-topology, double-pointed-cofinite-topology, finite-cofinite-algebra]
sources:
  - wikipedia: en:382708@r1342057591
    locator: Cofiniteness
    note: adopted
    mention: wikipedia://en/382708
    sections: [Summary]
same_as:
  wikidata: Q3491998
  wikipedia: Cofiniteness
inventory: [SBZFHC4BKB]
---

## Summary

In mathematics, a **cofinite** [[subset|0BJR9QR08E]] of a set $X$ is a subset $A$ whose [[complement|0RKF1ZT5JJ]] in $X$ is a [[finite set|070R982G4B]]. In other words, $A$ contains all but finitely many elements of $X.$ If the complement is not finite, but is countable, then one says the set is cocountable.