Principia Mathematica, Volume 1

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Cambridge University Press, 1927 - Logic, Symbolic and mathematical
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Contents

1AGE
1
SERIES continued 250 Elementary properties of wellordered series
4
251 Ordinal numbers
18
252 Segments of wellordered aeries
27
253 Sectional relations of wellordered series
32
254 Qreater and less among wellordered series
44
255 Greater and less among ordinal numbers
58
256 The series of ordinals
73
306 Addition of simple ratios
289
307 Generalized ratios
296
308 Addition of generalized ratios
299
309 Multiplication of generalized ratios
309
310 The series of real numbers 316
316
311 Addition of concordant real numbers
320
312 Algebraic addition of real number
327
313 Multiplication of real numbers
333

257 The transfinite ancestnvl relation
81
258 Zermelos theorem
96
259 Inductively defined correlations
102
SECTION E FINITE AND INFINITE SERIES AND ORDINALS
108
260 On finite intervals in a series
109
261 Finite and infinite series
118
262 Finite ordinals
131
263 Progressions
143
264 Derivatives of wellordered series
156
265 The series of alephs
169
SECTION F COMPACT SERIES RATIONAL SERIES AND CONTINUOUS SERIES
179
270 Compact series
180
271 Median classes in series _
186
272 Similarity of position
191
273 Rational series
199
274 On series of finite subclasses of a series
207
275 Continuous series
218
276 On series of infinite subulasses of a series
221
QUANTITY
231
Summary of Part VI
233
SECTION A GENERALIZATION OF NUMBER
234
300 Positive and negative integers and numerical relations 235
235
301 Numerically defined powers of relations
244
302 On relative primes
251
303 Ratios
260
304 The series of ratios
278
305 Multiplication of simple ratios
283
314 Real numbers as relations
336
SECTION B VECTORFAMILIES
339
330 Elementary properties of vectorfamilies
350
331 Connected families
360
332 On the representative of relation in a family
367
333 Open families
376
334 Serial families
383
335 Initial families
390
336 The seriea of vectors
393
337 Multiples and aubroultiplca of vectors
403
MEASUREMENT
407
350 Ratios of members of a family
412
351 Submultipliable families
419
352 Rational multiples of a given vector
423
353 Rational families
431
354 Rational nets
436
356 Measurement by real numbers
443
359 Existencetheorems for vectorfamilies
452
CYCLIC FAMILIES
457
370 Elementary properties of cyclic families
462
371 The series of vectors
466
372 Integral sections of the series of vectors
470
373 Submultiplns of identity
475
374 Principal submultiples 435
485
375 Principal ration
487
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