Archimedean property

Common card · No. 230409

In abstract algebra and analysis, the Archimedean property, named after the ancient Greek mathematician Archimedes of Syracuse, is a property held by some algebraic structures, such as ordered or normed groups, and fields. The property, as typically construed, states that given two positive numbers x {\displaystyle x} and y {\displaystyle y} , there is a positive integer n {\displaystyle n} such that n x > y {\displaystyle nx>y} . The fact that the set of natural numbers satisfies the Archimedean property implies that the set of natural numbers is not bounded above. Roughly speaking, it is the property of having no infinitely large or infinitely small elements. It was Otto Stolz who gave the axiom of Archimedes its name because it appears as Axiom V of Archimedes’ On the Sphere and Cylinder...

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