Book:Alfred North Whitehead/Principia Mathematica/Volume 3

Subject Matter

 * Mathematical Logic

Contents

 * PREFACE TO VOLUME III


 * PART V. SERIES (continued).




 * $*$250. Elementary properties of well-ordered series
 * $*$251. Ordinal numbers
 * $*$252. Segments of well-ordered series
 * $*$253. Sectional relations of well-ordered series
 * $*$254. Greater and less among well-ordered series
 * $*$255. Greater and less among ordinal numbers
 * $*$256. The series of ordinals
 * $*$257. The transfinite ancestral relation
 * $*$258. Zermelo's theorem
 * $*$259. Inductively defined correlations




 * $*$260. On finite intervals in a series
 * $*$261. Finite and infinite series
 * $*$262. Finite ordinals
 * $*$263. Progressions
 * $*$264. Derivatives of well-ordered series
 * $*$265. The series of alephs




 * $*$270. Compact series
 * $*$271. Median classes in series
 * $*$272. Similarity of position
 * $*$273. Rational series
 * $*$274. On series of finite sub-classes of a series
 * $*$275. Continuous series
 * $*$276. On series of infinite sub-classes of a series


 * PART VI. QUANTITY
 * Summary of Part VI




 * $*$300. Positive and negative integers, and numerical relations
 * $*$301. Numerically defined powers of relations
 * $*$302. On relative primes
 * $*$303. Ratios
 * $*$304. The series of ratios
 * $*$305. Multiplication of simple ratios
 * $*$306. Addition of simple ratios
 * $*$307. Generalized ratios
 * $*$308. Addition of generalized ratios
 * $*$309. Multiplication of generalized ratios
 * $*$310. The series of real numbers
 * $*$311. Addition of concordant real numbers
 * $*$312. Algebraic addition of real numbers
 * $*$313. Multiplication of real numbers
 * $*$314. Real numbers as relations




 * $*$330. Elementary properties of vector-families
 * $*$331. Connected families
 * $*$332. On the representative of a relation in a family
 * $*$333. Open families
 * $*$334. Serial families
 * $*$335. Initial families
 * $*$336. The series of vectors
 * $*$337. Multiples and submultiples of vectors




 * $*$350. Ratios of members of a family
 * $*$351. Submultipliable families
 * $*$352. Rational multiples of a given vector
 * $*$353. Rational families
 * $*$354. Rational nets
 * $*$356. Measurement by real numbers
 * $*$359. Existence-theorems for vector-families




 * $*$370. Elementary properties of cyclic families
 * $*$371. The series of vectors
 * $*$372. Integral sections of the series of vectors
 * $*$373. Submultiples of identity
 * $*$374. Principal submultiples
 * $*$375. Principal ratios