Note 105 — Chapter V · THE WORLD OF THINGS—(2) CHANGE AND CAUSALITY

For a fuller explanation of what is meant by continuity, consult Dedekind, Stetigkeit und irrationale Zahlen, specially §§ 3-5, or Lamb’s Infinitesimal Calculus, chap. 1. Readers who have been accustomed to the treatment of continuity by the older philosophical writers should specially remark (1) that continuity is properly a characteristic of series, and (2) that though continuity implies indefinite divisibility, the reverse is not, as was sometimes assumed by earlier writers, true. The series of rational numbers is a familiar illustration of endless divisibility without continuity.