---
tag: 0XH79S06J3
kind: concept
name: Archimedean ordered field
msc: [12J15]
sources:
  - url: https://en.wikipedia.org/wiki/Archimedean_property
    locator: Ordered fields
---

## Summary

An Archimedean ordered field is an [[ordered field|0P3VCBDEE2]] that has no infinitely large and no infinitely small positive elements.
In such a field, the natural numbers are not bounded above.
The fields $\mathbb{Q}$ and $\mathbb{R}$ are Archimedean.