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Bibliographic Details
Main Author:	Niven, Ivan 1915-1999 (Author)
Format:	Book
Language:	English
Published:	Rahway, NJ Math. Assoc. of America 1967
Edition:	3. print.
Series:	Carus math. monographs. No. 11.
Subjects:	Irrationale Zahl Transzendente Zahl
Online Access:	Inhaltsverzeichnis
Physical Description:	XII, 164 S.

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MARC


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adam_text	CONTENTS CHAPTER PAGE I. Rationals and Irrationals 1. The preponderance of irrationals 1 2. Countability 4 3. Dense sets 5 4. Decimal expansions 6 II. Simple Irrationalities 1. Introduction 15 2. The trigonometric functions and r 16 3. The hyperbolic, exponential, and logarithmic functions. 22 III. Certain Algebraic Numbers 1. Introduction 28 2. Further background material 30 3. The factorization of x* - 1 33 4. Certain trigonometric values 36 5. Extension to the tangent 38 IV. The Approximation of Irrationals by Rationals 1. The problem 42 2. A generalization 44 3. Linearly dependent sets 48 V. Continued Fractions 1. The Euclidean algorithm 51 2. Uniqueness 53 3. Infinite continued fractions 54 4. Infinite continued fraction expansions 59 5. The convergents as approximations 61 6. Periodic continued fractions 63 VI. Further Diophantine Approximations 1. A basic result 68 2. Best possible approximations 70 xi Xii CONTENTS CHAPTER PAGE 3. Uniform distributions 71 4. A proof by Fourier analysis 75 VII. Algebraic and Transcendental, Numbers 1. Closure properties of algebraic numbers 83 2. A property of algebraic integers 85 3. Transcendental numbers 87 4. The order of approximation 88 VIII. Normal Numbers 1. Definition of a normal number 94 2. The measure of the set of normal numbers 98 3. Equivalent definitions 104 4. A normal number exhibited 112 IX. The Generalized Lindemann Theorem 1. Statement of the theorem 117 2. Preliminaries 118 3. Proof of the theorem 124 4. Applications of the theorem 131 5. Squaring the circle 132 X. The Gelfond-Schneider Theorem 1. Hilbert s seventh problem 134 2. Background material 135 3. Two lemmas 137 4. Proof of the Gelfond-Schneider theorem 142 List or Notation 151 Glossary 153 Reference Books 157 Index of Topics 159 Index of Names 163
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id	DE-604.BV005717563
illustrated	Not Illustrated
indexdate	2024-07-09T16:33:34Z
institution	BVB
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-003571436
oclc_num	257959371
open_access_boolean
owner	DE-703 DE-355 DE-BY-UBR DE-824
owner_facet	DE-703 DE-355 DE-BY-UBR DE-824
physical	XII, 164 S.
publishDate	1967
publishDateSearch	1967
publishDateSort	1967
publisher	Math. Assoc. of America
record_format	marc
series	Carus math. monographs.
series2	Carus math. monographs.
spelling	Niven, Ivan 1915-1999 Verfasser (DE-588)115101217 aut Irrational numbers 3. print. Rahway, NJ Math. Assoc. of America 1967 XII, 164 S. txt rdacontent n rdamedia nc rdacarrier Carus math. monographs. No. 11. Irrationale Zahl (DE-588)4162426-9 gnd rswk-swf Transzendente Zahl (DE-588)4225034-1 gnd rswk-swf Irrationale Zahl (DE-588)4162426-9 s Transzendente Zahl (DE-588)4225034-1 s 1\p DE-604 Carus math. monographs. No. 11. (DE-604)BV001887236 11 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003571436&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Niven, Ivan 1915-1999 Irrational numbers Carus math. monographs. Irrationale Zahl (DE-588)4162426-9 gnd Transzendente Zahl (DE-588)4225034-1 gnd
subject_GND	(DE-588)4162426-9 (DE-588)4225034-1
title	Irrational numbers
title_auth	Irrational numbers
title_exact_search	Irrational numbers
title_full	Irrational numbers
title_fullStr	Irrational numbers
title_full_unstemmed	Irrational numbers
title_short	Irrational numbers
title_sort	irrational numbers
topic	Irrationale Zahl (DE-588)4162426-9 gnd Transzendente Zahl (DE-588)4225034-1 gnd
topic_facet	Irrationale Zahl Transzendente Zahl
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003571436&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV001887236
work_keys_str_mv	AT nivenivan irrationalnumbers

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