Infinite Orbits Revisited

This is the first of four chapters giving a self-contained proof of Theorem 0.7. Section 23.2 describes a sequence of even rationals {pn/qn} that converges to A. Section 23.3 states the two main technical results, the Box Theorem and the Copy Theorem. Section 23.4 shows how to choose a sequence {cn}. Section 23.5 states three auxiliary results about arc copying in the plaid model. Section 23.6 deduces the Box Theorem from one of these auxiliary lemmas. Section 23.7 deduces the Copy Theorem from the auxiliary lemmas and some elementary number theory. Thus, after this chapter ends, the only remaining task is to prove the auxiliary copy lemmas and prove a few lemmas in elementary number theory.