# Book:Alfred North Whitehead/Principia Mathematica/Volume 2

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## Bertrand Russell and Alfred North Whitehead:

## Bertrand Russell and Alfred North Whitehead: *Principia Mathematica, Volume $\text { 2 }$*

Published $1912$, **Merchant Books**

- ISBN 987-1-60386-183-0.

### Subject Matter

### Contents

- PREFATORY STATEMENT OF SYMBOLIC CONVENTIONS

- PART III. CARDINAL ARITHMETIC
- Summary of Part III

- Section A. Definition and Logical Properties of Cardinal Numbers

- $*$100. Definition and elementary properties of cardinal numbers
- $*$101. On $0$ and $1$ and $2$
- $*$102. On cardinal numbers of assigned types
- $*$103. Homogeneous cardinals
- $*$104. Ascending cardinals
- $*$105. Descending cardinals
- $*$106. Cardinals of relation types

- Section B. Addition, Multiplication and Exponentiation

- $*$110. The arithmetical sum of two classes and of two cardinals
- $*$111. Double similarity
- $*$112. The arithmetical sum of a class of classes
- $*$113. On the arithmetical product of two classes or of two cardinals
- $*$114. The arithmetical product of a class of classes
- $*$115. Multiplicative classes and arithmetical classes
- $*$116. Exponentiation
- $*$117. Greater and less
- General note on cardinal correlators

- Section C. Finite and Infinite

- $*$118. Arithmetical substitution and uniform formal numbers
- $*$119. Subtraction
- $*$120. Inductive cardinals
- $*$121. Intervals
- $*$122. Progressions
- $*$123. $\aleph_0$
- $*$124. Reflexive classes and cardinals
- $*$125. The axiom of infinity
- $*$126. On typically indefinite inductive cardinals

- PART IV. RELATIONAL ARITHMETIC
- Summary of Part IV

- Section A. Ordinal Similarity and Relation-Numbers

- $*$150. Internal transformations of a relation
- $*$151. Ordinal similarity
- $*$152. Definition and elementary properties of relation-numbers
- $*$153. The relation-numbers $0_r$, $2_r$ and $1_s$
- $*$154. Relation-numbers of assigned types
- $*$155. Homogeneous relation-numbers

- Section B. Addition of Relations, and the product of two relations

- $*$160. The sum of two relations
- $*$161. Addition of a term to a relation
- $*$162. The sum of the relations of a field
- $*$163. Relations of mutually exclusive relations
- $*$164. Double likeness
- $*$165. Relations of relations of couples
- $*$166. The product of two relations

- Section C. The Principle of First Differences, and the multiplication and exponentiation of relations

- $*$170. On the relation of first differences among the sub-classes of a given class
- $*$171. The principle of first differences (continued)
- $*$172. The product of the relations of a field
- $*$173. The product of the relations of a field (continued)
- $*$174. The associative law of relational multiplication
- $*$176. Exponentiation
- $*$177. Propositions connecting $P_{\mathrm d f}$ with products and powers

- Section D. Arithmetic of Relation-Numbers

- $*$180. The sum of two relation-numbers
- $*$181. On the addition of unity to a relation-number
- $*$182. On separated relations
- $*$183. The sum of the relation-numbers of a field
- $*$184. The product of two relation-numbers
- $*$185. The product of the relation-numbers of a field
- $*$186. Powers of relation-numbers

- PART V. SERIES
- Summary of Part V

- Section A. General Theory of Series

- $*$200. Relations contained in diversity
- $*$201. Transitive relations
- $*$202. Connected relations
- $*$204. Elementary properties of series
- $*$205. Maximum and minimum points
- $*$206. Sequent points
- $*$207. Limits
- $*$208: The correlation of series

- Section B. On Sections, Segments, Stretches and Derivatives

- $*$210. On series of classes generated by the relation of inclusion
- $*$211. On sections and segments
- $*$212. The series of segments
- $*$213. Sectional relations
- $*$214. Dedekindian relations
- $*$215. Stretches
- $*$216. Derivatives
- $*$217. On segments of sums and converses

- Section C. On Convergence, and the Limits of Functions

- $*$230. On convergents
- $*$231. Limiting sections and ultimate oscillation of a function
- $*$232. On the oscillation of a function as the argument approaches a given limit
- $*$233. On the limits of functions
- $*$234. Continuity of functions