a crucial role for the real-number system has been that it provides a necessary framework for the standard formulation of the calculus (see Chapter 6). All successful dynamical theories have required notions of the calculus for their formulations. Now, the conventional approach to calculus requires the infinitesimal nature of the reals to be what it is. That is to say, on the small end of the scale, it is the entire range of the real numbers that is in principle being made use of. The ideas of calculus underlie other physical notions, such as velocity, momentum, and energy. Consequently, the
...more
