Archimedean property [SEP] named after
Archimedean property
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. 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".
The notion arose from the theory of
Archimedean group
In abstract algebra, a branch of mathematics, an Archimedean group is a linearly ordered group for which the Archimedean property holds: every two positive group elements are bounded by integer multiples of each other. The set R of real numbers together with the operation of addition and the usual ordering relation between pairs of numbers is an Archimedean group. By a result of Otto Hölder, every Archimedean group is isomorphic to a subgroup of this group. The name "Archimedean" comes from Otto Stolz, who named the Archimedean