Sets and transfinite numbers:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Macmillan [u.a.]
1974
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 423 S. graph. Darst. |
| ISBN: | 0024321109 |
Staff View
MARC
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| 100 | 1 | |a Zuckerman, Martin M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Sets and transfinite numbers |c Martin M. Zuckerman |
| 264 | 1 | |a New York |b Macmillan [u.a.] |c 1974 | |
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Record in the Search Index
| _version_ | 1804117343512559616 |
|---|---|
| adam_text | Contents
Usage and Organization of the Book
1
The Basic Axioms of
Set Theory
1.1 Elements and Subsets
1.2 Language of Set Theory
1.3 Truth 16
24
1.4 Specification of Subsets
1.5 Axioms of Null Set, Pairing, and Union
29 •¦
1.6 Natural Numbers
35
1.7 Axiom of Power Set
1.8 Algebra of Sets
ix
x Contents
2
Relations
2.1 Ordered Pairs 43
2.2 Cartesian Products 45
2.3 Binary Relations 49
2.4 Functions 54
2.5 Equivalence Relations 60
2.6 Orderings 65
2.7 Well orderings 73
2.8 Binary Operations 78
3
Real and Complex Numbers
as Sets
3.1 Introduction 83
3.2 Addition and Multiplication of Natural Numbers 85
3.3 Fundamental Theorem of Arithmetic 88
3.4 Integers 92
3.5 Integers as Equivalence Classes 100
3.6 Rational Numbers 104
3.7 Arithmetic of Rational Numbers 107
3.8 Ordering the Rational Numbers 112
3.9 Real Numbers as Dedekind Cuts 116
3.10 Arithmetic and Ordering of Real Numbers 120
3.11 Complex Numbers: Intuitive Approach 131
3.12 Complex Numbers as Sets 135
4
Denumerability and Choice
4.1 Finite Sets; Infinite Sets 141
4.2 Axiom of Choice 146
4.3 Denumerable Unions, Intersections, and Products 149
4.4 Sequences, A/ tuples, and/V place Relations 152
Contents xi
4.5 Denumerability of Rational Numbers 155
4.6 Nondenumerability of Real Numbers 157
4.7 Some Equivalents of the Axiom of Choice 165
4.8 Well ordering Theorem 169
5
Ordinal Numbers
5.1 Similarity Mappings 175
5.2 Ordinal Numbers 181
5.3 Axiom of Substitution 190
5.4 Definition by Transfinite Induction 199
5.5 Ordinal Addition . 203
5.6 Ordinal Multiplication 212
5.7 Ordinal Subtraction and Division 219
5.8 Ordinal Exponentiation 225
5.9 Transfinite Addition 229
5.10 Transfinite Multiplication 242
5.11 Cantor Normal Form 247
5.12 Denumerable Ordinal Numbers 255
5.13 Maximal Principles 261
6
Order Types and
Cardinal Numbers
6.1 Rank 267
6.2 Order Types 273
6.3 Arithmetic of Order Types 283
6.4 Cardinal Numbers 289
6.5 Cardinal Addition and Multiplication 296
6.6 Cardinal Exponentiation 301
6.7 Alephs 307
6.8 Aleph Arithmetic 312
6.9 Cardinal Numbers and the Axiom of Choice 320
xii Contents
6.10 Transfinite Addition and Multiplication of Cardinal Numbers 329
6.11 Ordinal Cofinality 338
6.12 Generalized Continuum Hypothesis 349
Bibliography 363
Selected Answers and Hints 367
List of Symbols 401
Index 411
|
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| id | DE-604.BV003054485 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:52:54Z |
| institution | BVB |
| isbn | 0024321109 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001914041 |
| oclc_num | 299380503 |
| open_access_boolean | |
| owner | DE-384 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-29T DE-83 DE-188 |
| owner_facet | DE-384 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-29T DE-83 DE-188 |
| physical | XVI, 423 S. graph. Darst. |
| publishDate | 1974 |
| publishDateSearch | 1974 |
| publishDateSort | 1974 |
| publisher | Macmillan [u.a.] |
| record_format | marc |
| spelling | Zuckerman, Martin M. Verfasser aut Sets and transfinite numbers Martin M. Zuckerman New York Macmillan [u.a.] 1974 XVI, 423 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Transfinite Zahl (DE-588)4471005-7 gnd rswk-swf Menge (DE-588)4038613-2 gnd rswk-swf Transfinite Zahl (DE-588)4471005-7 s Menge (DE-588)4038613-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001914041&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zuckerman, Martin M. Sets and transfinite numbers Transfinite Zahl (DE-588)4471005-7 gnd Menge (DE-588)4038613-2 gnd |
| subject_GND | (DE-588)4471005-7 (DE-588)4038613-2 |
| title | Sets and transfinite numbers |
| title_auth | Sets and transfinite numbers |
| title_exact_search | Sets and transfinite numbers |
| title_full | Sets and transfinite numbers Martin M. Zuckerman |
| title_fullStr | Sets and transfinite numbers Martin M. Zuckerman |
| title_full_unstemmed | Sets and transfinite numbers Martin M. Zuckerman |
| title_short | Sets and transfinite numbers |
| title_sort | sets and transfinite numbers |
| topic | Transfinite Zahl (DE-588)4471005-7 gnd Menge (DE-588)4038613-2 gnd |
| topic_facet | Transfinite Zahl Menge |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001914041&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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