Non-Archimedean
Encyclopedia
In mathematics and physics, non-Archimedean refers to something without the Archimedean property
. This includes:
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...
. This includes:
- Ultrametric space
- notably, p-adic numbers
- Non-Archimedean ordered fieldNon-Archimedean ordered fieldIn mathematics, a non-Archimedean ordered field is an ordered field that does not satisfy the Archimedean property. Examples are the Levi-Civita field, the hyperreal numbers, the surreal numbers, the Dehn field, and the field of rational functions with real coefficients with a suitable...
, namely:- Levi-Civita fieldLevi-Civita fieldIn mathematics, the Levi-Civita field, named after Tullio Levi-Civita, is a non-Archimedean ordered field, i.e., a system of numbers containing infinite and infinitesimal quantities...
- Hyperreal numbers
- Surreal numbers
- Dehn planes
- Levi-Civita field
- In theoretical physics, Non-Archimedean timeNon-archimedean timeA non-Archimedean time theory of time is any theory that holds that there exist instants infinitely in the future or infinitely in the past. It is so called because, if the instants of such time are assigned numbers, the set of such numbers must be non-Archimedean.Non-Archimedean future time would...