---
tag: 0MSSD1VCW9
kind: concept
name: Order on the reals
msc: [26A03]
sources:
  - url: https://en.wikipedia.org/wiki/Construction_of_the_real_numbers
    locator: Construction from Cauchy sequences
  - url: https://en.wikipedia.org/wiki/Real_number
    locator: Auxiliary order relations
---

## Summary

The order on the reals is the relation $\le$ on $\mathbb{R}$ that compares two real numbers by their position on the number line.
It extends the order of $\mathbb{Q}$ and makes $\mathbb{R}$ an [[ordered field|010JCV9J4E]].