Definitions for archimedean property
ar·chi·me·dean prop·er·ty

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1. Archimedean propertynoun

   The property of the set of real numbers, that for any real number there is always a natural number greater than that real number.

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1. 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. The property, typically construed, states that given two positive numbers x {\displaystyle x} and y {\displaystyle y} , there is an integer n {\displaystyle n} such that n x > y {\displaystyle nx>y} . It also means 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.The notion arose from the theory of magnitudes of Ancient Greece; it still plays an important role in modern mathematics such as David Hilbert's axioms for geometry, and the theories of ordered groups, ordered fields, and local fields. An algebraic structure in which any two non-zero elements are comparable, in the sense that neither of them is infinitesimal with respect to the other, is said to be Archimedean. A structure which has a pair of non-zero elements, one of which is infinitesimal with respect to the other, is said to be non-Archimedean. For example, a linearly ordered group that is Archimedean is an Archimedean group. This can be made precise in various contexts with slightly different formulations. For example, in the context of ordered fields, one has the axiom of Archimedes which formulates this property, where the field of real numbers is Archimedean, but that of rational functions in real coefficients is not.

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1. 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 ordered or normed groups, fields, and other algebraic structures. 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 magnitudes of Ancient Greece; it still plays an important role in modern mathematics such as David Hilbert's axioms for geometry, and the theories of ordered groups, ordered fields, and local fields. An algebraic structure in which any two non-zero elements are comparable, in the sense that neither of them is infinitesimal with respect to the other, is said to be Archimedean. A structure which has a pair of non-zero elements, one of which is infinitesimal with respect to the other, is said to be non-Archimedean. For example, a linearly ordered group that is Archimedean is an Archimedean group. This can be made precise in various contexts with slightly different ways of formulation. For example, in the context of ordered fields, one has the axiom of Archimedes which formulates this property, where the field of real numbers is Archimedean, but that of rational functions in real coefficients is not.

How to pronounce archimedean property?

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How to say archimedean property in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of archimedean property in Chaldean Numerology is: 1

2. Pythagorean Numerology

   The numerical value of archimedean property in Pythagorean Numerology is: 7

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Archimedean_Property
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Archimedean_Property
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=archimedean property