Book:Alfred North Whitehead/Principia Mathematica/Volume 3

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Alfred North Whitehead and Bertrand Russell: Principia Mathematica, Volume 3

Published $1913$, Merchant Books

ISBN 978-1-60386-194-7.


Subject Matter


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