Foundations of Constructive Mathematics: Metamathematical Studies
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1985
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics
6 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is about some recent work in a subject usually considered part of "logic" and the" foundations of mathematics", but also having close connections with philosophy and computer science. Namely, the creation and study of "formal systems for constructive mathematics". The general organization of the book is described in the" User's Manual" which follows this introduction, and the contents of the book are described in more detail in the introductions to Part One, Part Two, Part Three, and Part Four. This introduction has a different purpose; it is intended to provide the reader with a general view of the subject. This requires, to begin with, an elucidation of both the concepts mentioned in the phrase, "formal systems for constructive mathematics". "Constructive mathematics" refers to mathematics in which, when you prove that l a thing exists (having certain desired properties) you show how to find it. Proof by contradiction is the most common way of proving something exists without showing how to find it - one assumes that nothing exists with the desired properties, and derives a contradiction. It was only in the last two decades of the nineteenth century that mathematicians began to exploit this method of proof in ways that nobody had previously done; that was partly made possible by the creation and development of set theory by Georg Cantor and Richard Dedekind |
| Beschreibung: | 1 Online-Ressource (XXIII, 466p) |
| ISBN: | 9783642689529 9783642689543 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-642-68952-9 |
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Datensatz im Suchindex
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| author | Beeson, Michael J. |
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| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-68952-9 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642689529 9783642689543 |
| issn | 0071-1136 |
| language | English |
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| physical | 1 Online-Ressource (XXIII, 466p) |
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| publishDate | 1985 |
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| publisher | Springer Berlin Heidelberg |
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| series | Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics |
| spelling | Beeson, Michael J. Verfasser aut Foundations of Constructive Mathematics Metamathematical Studies by Michael J. Beeson Berlin, Heidelberg Springer Berlin Heidelberg 1985 1 Online-Ressource (XXIII, 466p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics 6 0071-1136 This book is about some recent work in a subject usually considered part of "logic" and the" foundations of mathematics", but also having close connections with philosophy and computer science. Namely, the creation and study of "formal systems for constructive mathematics". The general organization of the book is described in the" User's Manual" which follows this introduction, and the contents of the book are described in more detail in the introductions to Part One, Part Two, Part Three, and Part Four. This introduction has a different purpose; it is intended to provide the reader with a general view of the subject. This requires, to begin with, an elucidation of both the concepts mentioned in the phrase, "formal systems for constructive mathematics". "Constructive mathematics" refers to mathematics in which, when you prove that l a thing exists (having certain desired properties) you show how to find it. Proof by contradiction is the most common way of proving something exists without showing how to find it - one assumes that nothing exists with the desired properties, and derives a contradiction. It was only in the last two decades of the nineteenth century that mathematicians began to exploit this method of proof in ways that nobody had previously done; that was partly made possible by the creation and development of set theory by Georg Cantor and Richard Dedekind Mathematics Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Konstruktive Mathematik (DE-588)4165105-4 gnd rswk-swf Konstruktive Mathematik (DE-588)4165105-4 s 1\p DE-604 Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics 6 (DE-604)BV036692629 6 https://doi.org/10.1007/978-3-642-68952-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Beeson, Michael J. Foundations of Constructive Mathematics Metamathematical Studies Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics Mathematics Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Konstruktive Mathematik (DE-588)4165105-4 gnd |
| subject_GND | (DE-588)4165105-4 |
| title | Foundations of Constructive Mathematics Metamathematical Studies |
| title_auth | Foundations of Constructive Mathematics Metamathematical Studies |
| title_exact_search | Foundations of Constructive Mathematics Metamathematical Studies |
| title_full | Foundations of Constructive Mathematics Metamathematical Studies by Michael J. Beeson |
| title_fullStr | Foundations of Constructive Mathematics Metamathematical Studies by Michael J. Beeson |
| title_full_unstemmed | Foundations of Constructive Mathematics Metamathematical Studies by Michael J. Beeson |
| title_short | Foundations of Constructive Mathematics |
| title_sort | foundations of constructive mathematics metamathematical studies |
| title_sub | Metamathematical Studies |
| topic | Mathematics Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Konstruktive Mathematik (DE-588)4165105-4 gnd |
| topic_facet | Mathematics Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Konstruktive Mathematik |
| url | https://doi.org/10.1007/978-3-642-68952-9 |
| volume_link | (DE-604)BV036692629 |
| work_keys_str_mv | AT beesonmichaelj foundationsofconstructivemathematicsmetamathematicalstudies |