If you work with asymptotic notations enough you realise they can often (loosely) be used like numbers - they obey certain arithmetic laws, and it's not uncommon for analysts to write stuff like 2^o(1), for instance. Take that rabbit hole further and you get the hyperreals! A number system that at once generalises real numbers, asymptotic notation and infinitesimal/infinite quantities =D
https://en.m.wikipedia.org/wiki/Hyperreal_number
(for anyone who cares, the ultrafilter construction kinda bakes in the laws of asymptotics into its definition of equality, if you squint)