Principia Mathematica, Volume 3

Alfred North Whitehead, Bertrand Russell

University Press, 1913 - Logic, Symbolic and mathematical

Contents

• SERIES continued: 1
• 261: 17
• 251 Ordinal numbers: 26
• 253 Sectional relations of wellordered series: 41
• 254 Greater and less among wellordered series: 57
• 255 Greater and less among ordinal numbers: 69
• 256 The series of ordinals: 79
• 259 Inductively defined correlations: 107
• 108: 149
• 263 Progressions: 156
• 265 The series of alephs: 175
• Summary of Part VI: 233
• SECTION B VECTORFAMILIES: 339
• 330 Elementary properties of vectorfamilies: 359
• 332 On the representative of a relation in a family: 373
• 333 Open families: 379
• 334 Serial families: 385
• 336 The series of vectors: 394
• MEASUREMENT: 407
• 359: 452
• 374 Principal submultiples: 463
• 371 The series of vectors: 473
• 375 Principal ratios: 491

Popular passages

Page 233 - ... a class of one-one relations all having the same converse domain, and all having their domain contained in their converse domain. In such a case as spatial distances, the applicability of this view is obvious ; in such a case as masses, the view becomes applicable by considering eg one gramme as + one gramme, ie as the relation of a mass m to a mass m' when m exceeds m' by one gramme. What is commonly called simply one gramme will then be the mass which has the relation + one gramme to the zero...‎

Page v - We have developed a theory of ratios and real numbers which is prior to our theory of measurement, and yet is not purely arithmetical, ie does not treat ratios as mere couples of integers, but as relations between actual quantities such as two distances or two periods of time.‎

Bibliographic information

• Title: Principia Mathematica, Volume 3; Principia Mathematica, Alfred North Whitehead
• Authors: Alfred North Whitehead, Bertrand Russell
• Edition: 2
• Publisher: University Press, 1913
• Original from: the University of Michigan
• Digitized: Nov 23, 2005