# Exponentially closed field

In mathematics, an exponentially closed field is an ordered field ${\displaystyle F\,}$ which has an order preserving isomorphism ${\displaystyle E\,}$ of the additive group of ${\displaystyle F\,}$ onto the multiplicative group of positive elements of ${\displaystyle F\,}$ such that ${\displaystyle 1+1/n for some natural number ${\displaystyle n\,}$.

Isomorphism ${\displaystyle E\,}$ is called an exponential function in ${\displaystyle F\,}$.