User:Barto/Asymptotic Notation/Asymptotic Equivalence

Sketchy definition: $f\sim g\iff f-g=o(g)$. (Provably equivalent to $f-g=o(f)$.)

In case of field and if $g\neq0$ in a certain domain: equivalent to $f/g\to0$ (With appropriate definition of the limit in case of $\infty$.)