### Chapter XXIV. The Genesis of Series

### Chapter XXV. The Meaning of Order

- § 195. What is order?
- § 196. Three theories of
*between* - § 197. First theory
- § 198. A relation is not
*between*its terms - § 199. Second theory of
*between* - § 200. There appear to be ultimate triangular relations
- § 201. Reasons for rejecting the second theory
- § 202. Third theory of
*between*to be rejected - § 203. Meaning of separation of couples
- § 204. Reduction to transitive asymmetrical relations
- § 205. This reduction is formal
- § 206. But is the reason why separation leads to order
- § 207. The second way of generating series is alone fundamental, and gives the meaning of order

### Chapter XXVI. Asymmetrical Relations

- § 208. Classification of relations as regards symmetry and transitiveness
- § 209. Symmetrical transitive relations
- § 210. Reflexiveness and the principle of abstraction
- § 211. Relative position
- § 212. Are relations reducible to predications?
- § 213. Monadistic theory of relations
- § 214. Reasons for rejecting the theory
- § 215. Monistic theory and the reasons for rejecting it
- § 216. Order requires that relations should be ultimate

### Chapter XXVII. Difference of Sense and Difference of Sign

### Chapter XXVIII. On the Difference Between Open and Closed Series

### Chapter XXIX. Progressions and Ordinal Numbers

### Chapter XXX. Dedekind's Theory of Number

- § 234. Dedekind's principal ideas
- § 235. Representation of a system
- § 236. The notion of a
*chain* - § 237. The chain of an element
- § 238. Generalized form of mathematical induction
- § 239. Definition of a singly infinite system
- § 240. Definition of cardinals
- § 241. Dedekind's proof of mathematical induction
- § 242. Objections to his definition of ordinals
- § 243. And of cardinals

### Chapter XXXI. Distance

The Principles of Mathematics was written by Bertrand Russell, and published in in 1903. It is now available in the Public Domain.