This is the second part dedicated to § 4. In this second part, we draw the attention to some consequences of the definition of order. Namely, the existence of a modulus. We provide elementary properties of the modulus and, most importantly, mention both the triangle and inverse triangle inequality, the name of which will be more properly justified later on. The other half of this episode in concerned with the size or proportion of the natural numbers that have been identified last time in the set of reals. This size can be fixed introducing the so-called Archimedean axiom basically telling that always finitely many rocks will fit a given suitcase. The consequences of the Archimedean axiom together with the modulus will play the major role in the next episode, when we talk about sequences and convergence.