non-Archimedean field
C41932
concept
A non-Archimedean field is a field equipped with an absolute value or valuation that satisfies the ultrametric (strong triangle) inequality, making all sufficiently small elements infinitesimally small compared to 1 and violating the Archimedean property.
All labels observed (2)
| Label | Occurrences |
|---|---|
| non-Archimedean field canonical | 2 |
| real-closed field | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: non-Archimedean field
Generated description
A non-Archimedean field is a field equipped with an absolute value or valuation that satisfies the ultrametric (strong triangle) inequality, making all sufficiently small elements infinitesimally small compared to 1 and violating the Archimedean property.
Instances (2)
| Instance | Via concept surface |
|---|---|
| p-adic numbers | — |
| Levi-Civita field | — |