Levi-Civita field

Named after Tullio Levi-Civita.

Levi-Civita field (plural Levi-Civita fields)

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