[antics]

Retric, look.

Do you realize that the whole point of asymptotic analysis is that _we do not care_ what integers we "really" deal with? These bounds specifically deal with sorting arbitrary data of unbounded size, and _no other assumptions_.

Do you understand? No assumption that we can use parallelism. No games with integers you see in "real life". None of that is relevant. You can't play games with practicalities to get a better bound. This is the general bound, and if you fiddle with it to get something else, you are changing the scope of the question to be something else entirely.

If you want to have a discussion about those other models, fine, but that's not the discussion we're having.

[Retric]

What your talking about is a type of overly simplified model that's irrelevant for actual computing. My point is there are other models out there. If you actually want the fastest algorithm out there you need to design it for actual hardware with finite data, cache, limited registers, limited ram, and sometime aproximating a real instruction set etc.

However, by changing your assumptions you can still use O notation with more complex models.

[antics]

Yes, everyone knows this. This is not helpful.