---
tag: JYB0CX854N
kind: concept
name: Reflexive closure
sources:
  - wikipedia: en:22603618@r1360406510
    locator: Reflexive closure
    note: adopted
    mention: wikipedia://en/22603618
    sections: [Summary]
same_as:
  wikidata: Q1637549
  wikipedia: Reflexive closure
inventory: [HVBMT5HKZ9]
---

## Summary

In mathematics, the **reflexive closure** of a [[binary relation|05AVARPXA2]] $R$ on a [[set|0BSJ7RQ9BW]] $X$ is the smallest [[reflexive relation|0X8NMST0J2]] on $X$ that contains $R$, i.e. the set $R \cup \{(x,x) \mid x \in X \}$.