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

Subject Matter

• Mathematical Logic

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