On Wikipedia, I found a definition of infinite and infinitesimal for linearly ordered groups that states the following:
$x$ is infinitesimal with respect to $y$ (or equivalently, $y$ is infinite with respect to $x$) if, for every natural number $n$, the multiple $nx$ is less than $y$.
The link: https://en.wikipedia.org/wiki/Archimedean_property#Definition_for_linearly_ordered_groups
Unfortunately, there is no source given. Does anyone know a good source for this definition?