Sufficiency for Physics

In this section we argue, in a few different but related ways, that combed generalized functions suffice to describe all physics. We mean this statement to include all classical physics and all observables quantities in quantum mechanics and quantum field theory. Note that we do not argue that the use of combed generalized functions is necessary, only that it is sufficient. There are a few ways in which one can argue this case, which we will present in what follows. It should be noted in passing that the limitation of the functions to the interval $[-\pi,\pi]$ is of no consequence for this discussion of the physics applications, as shown in Appendix A.