Book II · Chapter 20

Chapter 20: Congruence from Canonical Distance

Page 93 in the printed volume

the relevant chapter earned betweenness as a theorem from the ultrametric structure of τ³, verifying Tarski axioms T1–T3. This chapter earns congruence from the same canonical distance d(x,y) = 2^{-δ(x,y)} (II.D13, the relevant chapter). Two segments are congruent when their endpoints have equal ultrametric distance. the relevant theorem (II.T16) verifies all six Tarski congruence axioms C1–C6. Euclidean congruence emerges from a non-Archimedean base.