There's generally an assumption that the elementary values we're using fit into native hardware values, and that some elementary operations on those values can

There's generally an assumption that the elementary values we're using fit into native hardware values, and that some elementary operations on those values can be done in constant time (e.g. a CPU instruction). If you want to talk about something like supporting arbitrarily large integers or defining the memory of the physical computer we're using, we need to be explicit about that, because it changes a lot of things. After all, a finite-memory computer is not Turing complete, and everything it can compute can be computed in constant time. :)