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Principia Mathematica Vol. 2

Principia Mathematica Vol. 2

by Alfred North Whitehead

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About this eBook

Author
Russell, Bertrand, 1872-1970
Title
Principia mathematica, vol. 2 (of 3)
Original Publication
Cambridge: University Press, 1910, copyright 1912, copyright 1913.
Credits
Richard Tonsing, Laura Natal and the Online Distributed Proofreading Team at www.pgdp.net (This book was produced from images made available by the HathiTrust Digital Library.) In memoriam of Greg Newby.
Language
English
LoC Class
QA: Science: Mathematics
Subject
Mathematics -- Philosophy
Category
Text
Project Gutenberg
eBook-No. 78255
Release Date
March 20, 2026
Copyright
Public domain in the USA.

Contents

  1. 1.Untitled
  2. 2.Untitled
  3. 3.Untitled
  4. 4.PRINCIPIA MATHEMATICA
  5. 5.Untitled
  6. 6.CONTENTS OF VOLUME II
  7. 7.ADDITIONAL ERRATA TO VOLUME I.
  8. 8.PREFATORY STATEMENT OF SYMBOLIC CONVENTIONS — FOOTNOTES:
  9. 9.PART III. CARDINAL ARITHMETIC.
  10. 10.SECTION A. DEFINITION AND LOGICAL PROPERTIES OF CARDINAL NUMBERS. — FOOTNOTES:
  11. 11.*100. DEFINITION AND ELEMENTARY PROPERTIES OF CARDINAL NUMBERS.
  12. 12.*101. ON 0 AND 1 AND 2.
  13. 13.*102. ON CARDINAL NUMBERS OF ASSIGNED TYPES.
  14. 14.*103. HOMOGENEOUS CARDINALS.
  15. 15.*104. ASCENDING CARDINALS.
  16. 16.*105. DESCENDING CARDINALS.
  17. 17.*106. CARDINALS OF RELATIONAL TYPES.
  18. 18.SECTION B. ADDITION, MULTIPLICATION AND EXPONENTIATION.
  19. 19.*110. THE ARITHMETICAL SUM OF TWO CLASSES AND OF TWO CARDINALS.
  20. 20.*111. DOUBLE SIMILARITY.
  21. 21.*112. THE ARITHMETICAL SUM OF A CLASS OF CLASSES.
  22. 22.*113. ON THE ARITHMETICAL PRODUCT OF TWO CLASSES OR OF TWO CARDINALS. — FOOTNOTES:
  23. 23.*114. THE ARITHMETICAL PRODUCT OF A CLASS OF CLASSES.
  24. 24.*115. MULTIPLICATIVE CLASSES AND ARITHMETICAL CLASSES.
  25. 25.*116. EXPONENTIATION.
  26. 26.*117. GREATER AND LESS.
  27. 27.GENERAL NOTE ON CARDINAL CORRELATORS.
  28. 28.SECTION C. FINITE AND INFINITE. — FOOTNOTES:
  29. 29.*118. ARITHMETICAL SUBSTITUTION AND UNIFORM FORMAL NUMBERS.
  30. 30.*119. SUBTRACTION.
  31. 31.*120. INDUCTIVE CARDINALS.
  32. 32.*121. INTERVALS. — FOOTNOTES:
  33. 33.*122. PROGRESSIONS.
  34. 34.*123. .
  35. 35.*124. REFLEXIVE CLASSES AND CARDINALS.
  36. 36.*125. THE AXIOM OF INFINITY.
  37. 37.*126. ON TYPICALLY INDEFINITE INDUCTIVE CARDINALS.
  38. 38.PART IV. RELATION-ARITHMETIC.
  39. 39.SUMMARY OF PART IV. — FOOTNOTES:
  40. 40.SECTION A. ORDINAL SIMILARITY AND RELATION-NUMBERS.
  41. 41.*150. INTERNAL TRANSFORMATION OF A RELATION. — FOOTNOTES:
  42. 42.*151. ORDINAL SIMILARITY.
  43. 43.*152. DEFINITION AND ELEMENTARY PROPERTIES OF RELATION-NUMBERS.
  44. 44.*153. THE RELATION-NUMBERS , AND . — FOOTNOTES:
  45. 45.*154. RELATION-NUMBERS OF ASSIGNED TYPES.
  46. 46.*155. HOMOGENEOUS RELATION-NUMBERS. — FOOTNOTES:
  47. 47.SECTION B. ADDITION OF RELATIONS, AND THE PRODUCT OF TWO RELATIONS.
  48. 48.*160. THE SUM OF TWO RELATIONS.
  49. 49.*161. ADDITION OF A TERM TO A RELATION.
  50. 50.*162. THE SUM OF THE RELATIONS OF A FIELD.
  51. 51.*163. RELATIONS OF MUTUALLY EXCLUSIVE RELATIONS.
  52. 52.*164. DOUBLE LIKENESS.
  53. 53.*165. RELATIONS OF RELATIONS OF COUPLES.
  54. 54.*166. THE PRODUCT OF TWO RELATIONS.
  55. 55.SECTION C. THE PRINCIPLE OF FIRST DIFFERENCES, AND THE MULTIPLICATION AND EXPONENTIATION OF RELATIONS. — FOOTNOTES:
  56. 56.*170. ON THE RELATION OF FIRST DIFFERENCES AMONG THE SUB-CLASSES OF A GIVEN CLASS.
  57. 57.*171. THE PRINCIPLE OF FIRST DIFFERENCES ( continued ).
  58. 58.*172. THE PRODUCT OF THE RELATIONS OF A FIELD.
  59. 59.*173. THE PRODUCT OF THE RELATIONS OF A FIELD (continued).
  60. 60.*174. THE ASSOCIATIVE LAW OF RELATIONAL MULTIPLICATION.
  61. 61.*176. EXPONENTIATION.
  62. 62.*177. PROPOSITIONS CONNECTING WITH PRODUCTS AND POWERS.
  63. 63.SECTION D. ARITHMETIC OF RELATION-NUMBERS.
  64. 64.*180. THE SUM OF TWO RELATION-NUMBERS.
  65. 65.*181. ON THE ADDITION OF UNITY TO A RELATION-NUMBER.
  66. 66.*182 ON SEPARATED RELATIONS.
  67. 67.*183. THE SUM OF THE RELATION-NUMBERS OF A FIELD.
  68. 68.*184. THE PRODUCT OF TWO RELATION-NUMBERS.
  69. 69.*185. THE PRODUCT OF THE RELATION-NUMBERS OF A FIELD.
  70. 70.*186. POWERS OF RELATION-NUMBERS.
  71. 71.PART V. SERIES.
  72. 72.SUMMARY OF PART V.
  73. 73.SECTION A. GENERAL THEORY OF SERIES.
  74. 74.*200. RELATIONS CONTAINED IN DIVERSITY.
  75. 75.*201. TRANSITIVE RELATIONS.
  76. 76.*202. CONNECTED RELATIONS.
  77. 77.*204. ELEMENTARY PROPERTIES OF SERIES.
  78. 78.*205. MAXIMUM AND MINIMUM POINTS.
  79. 79.*206. SEQUENT POINTS.
  80. 80.*207. LIMITS.
  81. 81.*208. THE CORRELATION OF SERIES.
  82. 82.SECTION B. ON SECTIONS, SEGMENTS, STRETCHES, AND DERIVATIVES.
  83. 83.*210. ON SERIES OF CLASSES GENERATED BY THE RELATION OF INCLUSION.
  84. 84.*211. ON SECTIONS AND SEGMENTS.
  85. 85.*212. THE SERIES OF SEGMENTS.
  86. 86.*213. SECTIONAL RELATIONS.
  87. 87.*214. DEDEKINDIAN RELATIONS.
  88. 88.*215. STRETCHES.
  89. 89.*216. DERIVATIVES.
  90. 90.*217. ON SEGMENTS OF SUMS AND CONVERSES.
  91. 91.SECTION C. ON CONVERGENCE, AND THE LIMITS OF FUNCTIONS.
  92. 92.*230. ON CONVERGENTS.
  93. 93.*231. LIMITING SECTIONS AND ULTIMATE OSCILLATION OF A FUNCTION.
  94. 94.*232. ON THE OSCILLATION OF A FUNCTION AS THE ARGUMENT APPROACHES A GIVEN LIMIT.
  95. 95.*233. ON THE LIMITS OF FUNCTIONS.
  96. 96.*234. CONTINUITY OF FUNCTIONS. — FOOTNOTES:
  97. 97.Untitled

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