Levi-Civita field

English

Etymology

Named after Tullio Levi-Civita.

Noun

Levi-Civita field (plural Levi-Civita fields)

1. (mathematics) A non-Archimedean ordered field whose every member $a$ can be constructed as a formal series of the form $a=\sum _{q\in \mathbb {Q} }a_{q}\varepsilon ^{q},$ where $a_{q}$ are real numbers, $\mathbb {Q}$ is the set of rational numbers, and $\varepsilon$ is to be interpreted as a fixed positive infinitesimal.