An Axiom actually attributed to Eudoxus (Boyer 1968) which states that

Iff the appropriate one of following conditions is satisfied for Integers and :

- 1. If , then .
- 2. If , then .
- 3. If , then .

Archimedes' Lemma is sometimes also known as Archimedes' axiom.

**References**

Boyer, C. B. *A History of Mathematics.* New York: Wiley, p. 99, 1968.

© 1996-9

1999-05-25