1. The Archimedean property is related to the concept of cofinality. 2. The Archimedean property puts it on a somewhat firmer foundation. 3. But Cauchy completeness and the Archimedean property taken together are equivalent to the others. 4. Axiom 4 implies the Archimedean property . 5. They also provide an example of a " nonarchimedean field " ( see Archimedean property ). 6. Instead of continuity, an alternative axiom can be assumed that does not involve a precise equality, called the Archimedean property . 7. :A further remark : the last step above would tend to use the so-called Archimedean property of the real numbers. 8. Additionally, the Archimedean property stated as definition 4 of Euclid's book V is originally due not to Archimedes but to Eudoxus. 9. This is ruled out by the Archimedean property of the real numbers . talk ) 01 : 22, 27 December 2013 ( UTC) 10. Some proofs that 0.999 & = 1 rely on the Archimedean property of the real numbers : that there are no nonzero infinitesimals.
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