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

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

Published $\text {1912}$, Merchant Books

ISBN 987-1-60386-183-0.

### 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