Algr, you are committing a fundamental fallacy here. You made reference to the fact that people make their computations on a calculator or computer, which, you correctly point out, does not use the system of real numbers. This has nothing to do with any preference for an alternative number system, and everything to do with the limitations of the underlying electronics. When engineers built their various systems of arithmetic, they were not promoting their's as superior, but rather theirs was intended to be used as a close approximation to a mainstream mathematical number system. The floating point and double precision floating point numbers are supposed to be approximately real numbers. The unsigned and signed integers are approximations for the actual integers. etc.