Archimedean ordered group
= Archimedean ordered group
{c}
An <ordered group> is Archimedean when $a\ge1$ and $a^n\le b$ for all positive <integers> force $a=1$. In an additive <Abelian group> this excludes a positive element whose every integer multiple stays below one fixed bound. This generalizes the <Archimedean property> of the <real numbers>.