Covering 1.4 of Keisler's Elementary Calculus, "Slope and Velocity; The Hyperreal Line"
That chapter defines: A number $\epsilon$ is said to be infinitely small, infinitesimal, if: $-a < \epsilon < a$. And goes on to an introduction to the hyperreal line.
However, this definition seems to imply an infinitely small number ($\epsilon$) is one which is between $\pm a$, which seems to be a very large range if you choose, for example, $a = 1000$.
I'm obviously missing something obvious.