Archimedes' axiom

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Archimedes' axiom

[¦är·kə¦mēd‚ēz ′ak·sē·əm]
(mathematics)
References in periodicals archive ?
Hilbert's axioms come in five groups, the first four comprising the Axioms of (I) Incidence, (II) Order, (III) Congruence and (IV) the Parallel Postulate.
(The relations "to the right of" and "to the left of", which I have made use of here for clarity of statement, are easily definable from the primitive relations of Hilbert's axioms.) (6) A complete manifold satisifies this last axiom (or, equivalently, satisfies the axioms in Hilbert's Group V) as well as the axioms in Hilbert's first four groups.
Moore indicated some redundancy in Hilbert's axioms of order, which Hilbert took into consideration in the following editions (e.g.