Archimedean Property

Overview

The Archimedean property states that if $x,y\in {\mathbb{R}}^{+}$, then there exists a positive integer $n$ such that $nx>y$. This fundamental property usually follows from the completeness axiom.

Bibliography

• “Archimedean Property,” in Wikipedia, June 23, 2024, https://en.wikipedia.org/w/index.php?title=Archimedean_property.
• Tom M. Apostol, Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra, 2nd ed. (New York: Wiley, 1980).