---
tag: 0PWX18FM4G
kind: concept
name: Cauchy sequence
msc: [40A05]
sources:
  - url: https://en.wikipedia.org/wiki/Cauchy_sequence
    locator: lead section
same_as:
  wikidata: Q217847
  wikipedia: Cauchy sequence
---

## Summary

In a Cauchy sequence, any two terms with large enough indices are as near to each other as we wish. A metric space is complete when each Cauchy sequence in it converges, and the real numbers form a complete space. The node [[Cauchy sequence|0QZMTN5AXX]] gives the precise definition.