Book:Alfred North Whitehead/Principia Mathematica/Volume 3

Alfred North Whitehead and Bertrand Russell: Principia Mathematica, Volume $\text { 3 }$

Published $\text {1913}$, Merchant Books

ISBN 978-1-60386-194-7

Subject Matter

• Mathematical Logic

Contents

PREFACE TO VOLUME III

PART V. SERIES (continued).

Section D. Well-ordered Series

$*$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

Section E. Finite and Infinite Series and Ordinals

$*$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

Section F. Compact Series, Rational Series, and Continuous Series

$*$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

Section A. Generalization of Number

$*$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

Section B. Vector-Families

$*$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

Section C. Measurement

$*$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

Section D. Cyclic 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