Archimedean ordered field

Remarks

With $y = 1$, the definition gives the Archimedean property: for each $x$, some natural number exceeds $x$. Conversely, this property implies the definition. An equivalent condition: for each $\varepsilon > 0$ in $F$, there is a natural number $n \ge 1$ with $1/n < \varepsilon$. The field of rational functions $\mathbb{R}(t)$, with the order in which $t$ is larger than every real number, is not Archimedean.