[mikebenfield]

Big O notation deals with asymptotic behavior of a function - in other words, as N goes to infinity. If we're accepting the premise that N has an upper bound, the rest of the discussion is meaningless.

Presumably the argument is an abstract one, not applying to any particular machine that actually exists.

[charcircuit]

Big O notation is often used with assumptions like adding numbers is always constant time. You can't physically build a machine where addition between any two numbers is constant time, but that doesn't matter.

[xvedejas]

It depends what you mean by "numbers": all integers or just 64-bit ones?