By Volkodavov V.F., Radionova I.N., Bushkov S.V.

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But as instances of relations which do not have this property only two of our previous three instances will serve. If x is brother or sister of y, and y of z, x may not be brother or sister of z, since x and z may be the same person.

CONTENTS PREFACE EDITOR’S NOTE CHAPTER I: THE SERIES OF NATURAL NUMBERS CHAPTER II: DEFINITION OF NUMBER CHAPTER III: FINITUDE AND MATHEMATICAL INDUCTION CHAPTER IV: THE DEFINITION OF ORDER CHAPTER V: KINDS OF RELATIONS CHAPTER VI: SIMILARITY OF RELATIONS CHAPTER VII: RATIONAL, REAL, AND COMPLEX NUMBERS CHAPTER VIII: INFINITE CARDINAL NUMBERS CHAPTER IX: INFINITE SERIES AND ORDINALS CHAPTER X: LIMITS AND CONTINUITY CHAPTER XI: LIMITS AND CONTINUITY OF FUNCTIONS CHAPTER XII: SELECTIONS AND THE MULTIPLICATIVE AXIOM CHAPTER XIII: THE AXIOM OF INFINITY AND LOGICAL TYPES CHAPTER XIV: INCOMPATIBILITY AND THE THEORY OF DEDUCTION CHAPTER XV: PROPOSITIONAL FUNCTIONS CHAPTER XVI: DESCRIPTIONS CHAPTER XVII: CLASSES CHAPTER XVIII: MATHEMATICS AND LOGIC INDEX APPENDIX: CHANGES TO ONLINE EDITION PREFACE [page v] This book is intended essentially as an “Introduction,” and does not aim at giving an exhaustive discussion of the problems with which it deals.

The nature of infinity and continuity, for example, belonged in former days to philosophy, but belongs now to mathematics. Mathematical philosophy, in the strict sense, cannot, perhaps, be held to include such definite scientific results as have been obtained in this region; the philosophy of mathematics will naturally be expected to deal with questions on the frontier of knowledge, as to which comparative certainty is not yet attained. But speculation on such questions is hardly likely to be fruitful unless the more scientific parts of the principles of mathematics are known.