The mathematics of infinity: a guide to great ideas
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, N.J.
John Wiley & Sons
2012
|
| Ausgabe: | 2nd ed. |
| Schriftenreihe: | Pure and applied mathematics
|
| Schlagworte: | |
| Online-Zugang: | Publisher description Table of contents only Contributor biographical information Inhaltsverzeichnis |
| Beschreibung: | "Writing with clear knowledge and affection for the subject, the author introduces and explores infinite sets, infinite cardinals, and ordinals, thus challenging the readers' intuitive beliefs about infinity. Requiring little mathematical training and a healthy curiosity, the book presents a user-friendly approach to ideas involving the infinite. Readers will discover the main ideas of infinite cardinals and ordinal numbers without experiencing in-depth mathematical rigor. Classic arguments and illustrative examples are provided throughout the book and are accompanied by a gradual progression of sophisticated notions designed to stun your intuitive view of the world. Infinity, we are told, is as large as things get. This is not entirely true. This book does not refer to infinities, but rather to cardinals. This is to emphasize the point that what you thought you knew about infinity is probably incorrect or imprecise. Since the reader is assumed to be educated in mathematics, but not necessarily mathematically trained, an attempt has been made to convince the reader of the truth of a matter without resorting to the type of rigor found in professional journals. Therefore, the author has accompanied the proofs with illustrative examples. The examples are often a part of a larger proof. Important facts are included and their proofs have been excluded if the author has determined that the proof is beyond the scope of the discussion. For example, it is assumed and not proven within the book that a collection of cardinals is larger than any set or mathematical object. The topics covered within the book cannot be found within any other one book on infinity, and the work succeeds in being the only book on infinite cardinals for the high school educated person. Topical coverage includes: logic and sets; functions; counting infinite sets; infinite cardinals; well Includes bibliographical references and index |
| Beschreibung: | 358 S. |
| ISBN: | 9781118204481 |
Internformat
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV040328665 | ||
| 003 | DE-604 | ||
| 005 | 20120814 | ||
| 007 | t | ||
| 008 | 120724s2012 xxu |||| 00||| eng d | ||
| 010 | |a 2011041439 | ||
| 020 | |a 9781118204481 |9 978-1-11-820448-1 | ||
| 035 | |a (OCoLC)1039156587 | ||
| 035 | |a (DE-599)BVBBV040328665 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-20 | ||
| 050 | 0 | |a QA248 | |
| 082 | 0 | |a 511.3/22 | |
| 084 | |a SK 150 |0 (DE-625)143218: |2 rvk | ||
| 100 | 1 | |a Faticoni, Theodore G. |d 1954- |e Verfasser |0 (DE-588)172567610 |4 aut | |
| 245 | 1 | 0 | |a The mathematics of infinity |b a guide to great ideas |c Theodore G. Faticoni |
| 250 | |a 2nd ed. | ||
| 264 | 1 | |a Hoboken, N.J. |b John Wiley & Sons |c 2012 | |
| 300 | |a 358 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Pure and applied mathematics | |
| 500 | |a "Writing with clear knowledge and affection for the subject, the author introduces and explores infinite sets, infinite cardinals, and ordinals, thus challenging the readers' intuitive beliefs about infinity. Requiring little mathematical training and a healthy curiosity, the book presents a user-friendly approach to ideas involving the infinite. Readers will discover the main ideas of infinite cardinals and ordinal numbers without experiencing in-depth mathematical rigor. Classic arguments and illustrative examples are provided throughout the book and are accompanied by a gradual progression of sophisticated notions designed to stun your intuitive view of the world. Infinity, we are told, is as large as things get. This is not entirely true. This book does not refer to infinities, but rather to cardinals. This is to emphasize the point that what you thought you knew about infinity is probably incorrect or imprecise. Since the reader is assumed to be educated in mathematics, but not necessarily mathematically trained, an attempt has been made to convince the reader of the truth of a matter without resorting to the type of rigor found in professional journals. Therefore, the author has accompanied the proofs with illustrative examples. The examples are often a part of a larger proof. Important facts are included and their proofs have been excluded if the author has determined that the proof is beyond the scope of the discussion. For example, it is assumed and not proven within the book that a collection of cardinals is larger than any set or mathematical object. The topics covered within the book cannot be found within any other one book on infinity, and the work succeeds in being the only book on infinite cardinals for the high school educated person. Topical coverage includes: logic and sets; functions; counting infinite sets; infinite cardinals; well | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Cardinal numbers | |
| 650 | 4 | |a Set theory | |
| 650 | 4 | |a Infinite | |
| 650 | 7 | |a MATHEMATICS / Infinity |2 bisacsh | |
| 650 | 0 | 7 | |a Unendlichkeit |0 (DE-588)4136067-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mengenlehre |0 (DE-588)4074715-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kardinalzahl |0 (DE-588)4163318-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Mengenlehre |0 (DE-588)4074715-3 |D s |
| 689 | 0 | 1 | |a Unendlichkeit |0 (DE-588)4136067-9 |D s |
| 689 | 0 | 2 | |a Kardinalzahl |0 (DE-588)4163318-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy1201/2011041439-d.html |3 Publisher description | |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy1201/2011041439-t.html |3 Table of contents only | |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy1205/2011041439-b.html |3 Contributor biographical information | |
| 856 | 4 | 2 | |m LoC Fremddatenuebernahme |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025183134&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-025183134 | ||
Datensatz im Suchindex
| _version_ | 1804149359565078528 |
|---|---|
| adam_text | THE MATHEMATICS OF INFINITY
/ FATICONI, THEODORE GERARD
: C2012
TABLE OF CONTENTS / INHALTSVERZEICHNIS
1. LOGIC 1 1.1 AXIOMATIC METHOD 2 1.2 TABULAR LOGIC 3 1.3 TAUTOLOGY 9
1.4 LOGICAL STRATEGIES 15 1.5 IMPLICATIONS FROM IMPLICATIONS 17 1.6
UNIVERSAL QUANTIFIERS 20 1.7 FUN WITH LANGUAGE AND LOGIC 22 2. SETS 29
2.1 ELEMENTS AND PREDICATES 30 2.2 CARTESIAN PRODUCTS 45 2.3 POWER SETS
48 2.4 SOMETHING FROM NOTHING 50 2.5 INDEXED FAMILIES OF SETS 56 3.
FUNCTIONS 65 3.1 FUNCTIONAL PRELIMINARIES 66 3.2 IMAGES AND PREIMAGES 81
3.3 ONE-TO-ONE AND ONTO FUNCTIONS 90 3.4 BIJECTIONS 95 3.5 INVERSE
FUNCTIONS 97 4. COUNTING INFINITE SETS 105 4.1 FINITE SETS 105 4.2
HILBERT S INFINITE HOTEL 113 4.3 EQUIVALENT SETS AND CARDINALITY 128 5.
INFINITE CARDINALS 135 5.1 COUNTABLE SETS 136 5.2 UNCOUNTABLE SETS 149
5.3 TWO INFINITES 159 5.4 POWER SETS 166 5.5 THE ARITHMETIC OF CARDINALS
180 6. WELL ORDERED SETS 199 6.1 SUCCESSORS OF ELEMENTS 199 6.2 THE
ARITHMETIC OF ORDINALS 210 6.3 CARDINALS AS ORDINALS 222 6.4 MAGNITUDE
VERSUS CARDINALITY 234 7. INDUCTIONS AND NUMBERS 243 7.1 MATHEMATICAL
INDUCTION 243 7.2 SUMS OF POWERS OF INTEGERS 260 7.3 TRANSFINITE
INDUCTION 264 7.4 MATHEMATICAL RECURSION 274 7.5 NUMBER THEORY 279 7.6
THE FUNDAMENTAL THEOREM OF ARITHMETIC 283 7.7 PERFECT NUMBERS 285 8.
PRIME NUMBERS 289 8.1 PRIME NUMBER GENERATORS 289 8.2 THE PRIME NUMBER
THEOREM 292 8.3 PRODUCTS OF GEOMETRIC SERIES 296 8.4 THE RIEMANN ZETA
FUNCTION 302 8.5 REAL NUMBERS 307 9. LOGIC AND META-MATHEMATICS 313 9.1
THE COLLECTION OF ALL SETS 313 9.2 OTHER THAN TRUE OR FALSE 317 9.3
LOGICAL IMPLICATIONS OF A THEORY OF EVERYTHING 326 BIBLIOGRAPHY 283
INDEX 284 .
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Faticoni, Theodore G. 1954- |
| author_GND | (DE-588)172567610 |
| author_facet | Faticoni, Theodore G. 1954- |
| author_role | aut |
| author_sort | Faticoni, Theodore G. 1954- |
| author_variant | t g f tg tgf |
| building | Verbundindex |
| bvnumber | BV040328665 |
| callnumber-first | Q - Science |
| callnumber-label | QA248 |
| callnumber-raw | QA248 |
| callnumber-search | QA248 |
| callnumber-sort | QA 3248 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 150 |
| ctrlnum | (OCoLC)1039156587 (DE-599)BVBBV040328665 |
| dewey-full | 511.3/22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/22 |
| dewey-search | 511.3/22 |
| dewey-sort | 3511.3 222 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2nd ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>04008nam a2200541zc 4500</leader><controlfield tag="001">BV040328665</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20120814 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">120724s2012 xxu |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2011041439</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781118204481</subfield><subfield code="9">978-1-11-820448-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1039156587</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV040328665</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-20</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA248</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.3/22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 150</subfield><subfield code="0">(DE-625)143218:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Faticoni, Theodore G.</subfield><subfield code="d">1954-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)172567610</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The mathematics of infinity</subfield><subfield code="b">a guide to great ideas</subfield><subfield code="c">Theodore G. Faticoni</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2nd ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Hoboken, N.J.</subfield><subfield code="b">John Wiley & Sons</subfield><subfield code="c">2012</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">358 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Pure and applied mathematics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">"Writing with clear knowledge and affection for the subject, the author introduces and explores infinite sets, infinite cardinals, and ordinals, thus challenging the readers' intuitive beliefs about infinity. Requiring little mathematical training and a healthy curiosity, the book presents a user-friendly approach to ideas involving the infinite. Readers will discover the main ideas of infinite cardinals and ordinal numbers without experiencing in-depth mathematical rigor. Classic arguments and illustrative examples are provided throughout the book and are accompanied by a gradual progression of sophisticated notions designed to stun your intuitive view of the world. Infinity, we are told, is as large as things get. This is not entirely true. This book does not refer to infinities, but rather to cardinals. This is to emphasize the point that what you thought you knew about infinity is probably incorrect or imprecise. Since the reader is assumed to be educated in mathematics, but not necessarily mathematically trained, an attempt has been made to convince the reader of the truth of a matter without resorting to the type of rigor found in professional journals. Therefore, the author has accompanied the proofs with illustrative examples. The examples are often a part of a larger proof. Important facts are included and their proofs have been excluded if the author has determined that the proof is beyond the scope of the discussion. For example, it is assumed and not proven within the book that a collection of cardinals is larger than any set or mathematical object. The topics covered within the book cannot be found within any other one book on infinity, and the work succeeds in being the only book on infinite cardinals for the high school educated person. Topical coverage includes: logic and sets; functions; counting infinite sets; infinite cardinals; well</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Cardinal numbers</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Set theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Infinite</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Infinity</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Unendlichkeit</subfield><subfield code="0">(DE-588)4136067-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mengenlehre</subfield><subfield code="0">(DE-588)4074715-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kardinalzahl</subfield><subfield code="0">(DE-588)4163318-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Mengenlehre</subfield><subfield code="0">(DE-588)4074715-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Unendlichkeit</subfield><subfield code="0">(DE-588)4136067-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Kardinalzahl</subfield><subfield code="0">(DE-588)4163318-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="u">http://www.loc.gov/catdir/enhancements/fy1201/2011041439-d.html</subfield><subfield code="3">Publisher description</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="u">http://www.loc.gov/catdir/enhancements/fy1201/2011041439-t.html</subfield><subfield code="3">Table of contents only</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="u">http://www.loc.gov/catdir/enhancements/fy1205/2011041439-b.html</subfield><subfield code="3">Contributor biographical information</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">LoC Fremddatenuebernahme</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025183134&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-025183134</subfield></datafield></record></collection> |
| id | DE-604.BV040328665 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:21:47Z |
| institution | BVB |
| isbn | 9781118204481 |
| language | English |
| lccn | 2011041439 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025183134 |
| oclc_num | 1039156587 |
| open_access_boolean | |
| owner | DE-20 |
| owner_facet | DE-20 |
| physical | 358 S. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | John Wiley & Sons |
| record_format | marc |
| series2 | Pure and applied mathematics |
| spelling | Faticoni, Theodore G. 1954- Verfasser (DE-588)172567610 aut The mathematics of infinity a guide to great ideas Theodore G. Faticoni 2nd ed. Hoboken, N.J. John Wiley & Sons 2012 358 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics "Writing with clear knowledge and affection for the subject, the author introduces and explores infinite sets, infinite cardinals, and ordinals, thus challenging the readers' intuitive beliefs about infinity. Requiring little mathematical training and a healthy curiosity, the book presents a user-friendly approach to ideas involving the infinite. Readers will discover the main ideas of infinite cardinals and ordinal numbers without experiencing in-depth mathematical rigor. Classic arguments and illustrative examples are provided throughout the book and are accompanied by a gradual progression of sophisticated notions designed to stun your intuitive view of the world. Infinity, we are told, is as large as things get. This is not entirely true. This book does not refer to infinities, but rather to cardinals. This is to emphasize the point that what you thought you knew about infinity is probably incorrect or imprecise. Since the reader is assumed to be educated in mathematics, but not necessarily mathematically trained, an attempt has been made to convince the reader of the truth of a matter without resorting to the type of rigor found in professional journals. Therefore, the author has accompanied the proofs with illustrative examples. The examples are often a part of a larger proof. Important facts are included and their proofs have been excluded if the author has determined that the proof is beyond the scope of the discussion. For example, it is assumed and not proven within the book that a collection of cardinals is larger than any set or mathematical object. The topics covered within the book cannot be found within any other one book on infinity, and the work succeeds in being the only book on infinite cardinals for the high school educated person. Topical coverage includes: logic and sets; functions; counting infinite sets; infinite cardinals; well Includes bibliographical references and index Cardinal numbers Set theory Infinite MATHEMATICS / Infinity bisacsh Unendlichkeit (DE-588)4136067-9 gnd rswk-swf Mengenlehre (DE-588)4074715-3 gnd rswk-swf Kardinalzahl (DE-588)4163318-0 gnd rswk-swf Mengenlehre (DE-588)4074715-3 s Unendlichkeit (DE-588)4136067-9 s Kardinalzahl (DE-588)4163318-0 s DE-604 http://www.loc.gov/catdir/enhancements/fy1201/2011041439-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy1201/2011041439-t.html Table of contents only http://www.loc.gov/catdir/enhancements/fy1205/2011041439-b.html Contributor biographical information LoC Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025183134&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Faticoni, Theodore G. 1954- The mathematics of infinity a guide to great ideas Cardinal numbers Set theory Infinite MATHEMATICS / Infinity bisacsh Unendlichkeit (DE-588)4136067-9 gnd Mengenlehre (DE-588)4074715-3 gnd Kardinalzahl (DE-588)4163318-0 gnd |
| subject_GND | (DE-588)4136067-9 (DE-588)4074715-3 (DE-588)4163318-0 |
| title | The mathematics of infinity a guide to great ideas |
| title_auth | The mathematics of infinity a guide to great ideas |
| title_exact_search | The mathematics of infinity a guide to great ideas |
| title_full | The mathematics of infinity a guide to great ideas Theodore G. Faticoni |
| title_fullStr | The mathematics of infinity a guide to great ideas Theodore G. Faticoni |
| title_full_unstemmed | The mathematics of infinity a guide to great ideas Theodore G. Faticoni |
| title_short | The mathematics of infinity |
| title_sort | the mathematics of infinity a guide to great ideas |
| title_sub | a guide to great ideas |
| topic | Cardinal numbers Set theory Infinite MATHEMATICS / Infinity bisacsh Unendlichkeit (DE-588)4136067-9 gnd Mengenlehre (DE-588)4074715-3 gnd Kardinalzahl (DE-588)4163318-0 gnd |
| topic_facet | Cardinal numbers Set theory Infinite MATHEMATICS / Infinity Unendlichkeit Mengenlehre Kardinalzahl |
| url | http://www.loc.gov/catdir/enhancements/fy1201/2011041439-d.html http://www.loc.gov/catdir/enhancements/fy1201/2011041439-t.html http://www.loc.gov/catdir/enhancements/fy1205/2011041439-b.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025183134&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT faticonitheodoreg themathematicsofinfinityaguidetogreatideas |