Discrete physics with conservation and Galilean invariance

In this paper, we show how to avoid continuum concepts altogether for both Newtonian mechanics and for special relativistic mechanics. For Newtonian mechanics, we will establish all the usual conservation laws. For both Newtonian mechanics and for special relativistic mechanics, we will prove Galilean invariance for inertial systems. For easy comparison, discrete and continuous concepts will often be juxtaposed.