Nonstandard analysis

Contents......Page 7 Prologue......Page 11 Preface......Page 17 1.1 Infinitesimals and other nonstandard numbers:getting acquainted......Page 19 1.2 Other *-transforms; generating new numbers......Page 21 1.3 Bound and free variables; prenex normal form......Page 22 1.4 The purpose of nonstandard analysis......Page 25 1.5 More about the *-transform; transfer......Page 27 1.6 Standard, internal, and external constants......Page 30 1.7 Infinitesimals in Greek geometry?......Page 31 1.8 Infinitesimals in the 17th to the 19th century......Page 33 1.9 Infinitesimals in the 20th century......Page 36 1.10 Introducing infinitesimals by plausible reasonIng;filters......Page 39 1.11 Basic assumptions of formalism......Page 43 1.12 Basic assumptions of constructivism......Page 45 1.13 Selecting basic assumptions naively......Page 47 1.14 Basic definitions......Page 51 1.15 Filters......Page 53 1.16 About the nature of free ultrafilters......Page 55 2.1 Reviewing the introduction of Z,