Into infinity: discovering a world without end
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
RBA
2013
|
| Schriftenreihe: | Everything is mathematical
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | 140 S. Ill., graph. Darst. |
Internformat
MARC
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-025678503 | ||
Datensatz im Suchindex
| _version_ | 1804149998983577600 |
|---|---|
| adam_text | Contents
Prefoce
......................................................................................................................................................... 7
Chapter l.What is Infinity?
...................................................................................................... 9
Infinity in everyday life
.................................................................................................................... 9
A dictionary definition
...................................................................................................................... 11
Extremely large and extremely small
........................................................................................ 14
Apeiron
........................................................................................................................................................ 15
Potential infinity and actual infinity
......................................................................................... 17
Infinity in teaching
............................................................................................................................... 21
Chapter
2.
Discrete and Continuous
......................................................................,........... 25
Density
......................................................................................................................................................... 25
Discrete and continuous
................................................................................................................... 26
Trapping time
.......................................................................................................................................... 28
Zeno s paradoxes
.................................................................................................................................... 31
The dichotomy
............................................................................................................................... 33
Achilles and the tortoise
........................................................................................................... 33
The flying arrow
............................................................................................................................ 34
The stadium
..................................................................................................................................■.... 35
Squaring the circle
................................................................................................................................ 39
Irrational numbers
................................................................................................................................ 43
The quantum leap
................................................................................................................................ 47
Chapter
3.
Encounters with the Infinite
......................................................................... 51
Three-dimensional painting
........................................................................................................... 51
From perspective to projective
..................................................................................................... 53
Continuous transformations
........................................................................................................... 54
Quadratures
............................................................................................................................................... 58
Eudoxus
...................................................................................................................................................... 60
Kepler
......................................,................................................................................................................. 64
Galileo
........................................................................................................................................................ 66
Cavalieri
...................................................................................................................................................... 68
Descartes
................................................................................................,.................................................... 69
CONTENTS
Chapter
4.
Calculus
........................................................................................................................... 73
Infinitesimal analysis
............................................................................................................................ 73
Newton
........................................................................................................................................................ 76
Leibniz
........................................................................................................................................................ 78
Epsilons ........................................................................................................................................................ 85
Chapter
5.
Cantor s Paradise
..................................................................................................... 91
Fourier series
............................................................................................................................................ 91
Fundamental sequences
..................................................................................................................... 93
The real line
.............................................................................................................................................. 95
The cardinal numbers
......................................................................................................................... 96
Enumerable sets
...................................................................................................................................... 100
Beyond infinity
....................................................................................................................................... 103
Transcendental numbers
................................................................................................................... 106
Transfinite
numbers
............................................................................................................................. 110
The continuum hypothesis
............................................................................................................. 112
Chapter
6.
Cantor s Inferno
....................................................................................................... 117
Early years
.................................................................................................................................................. 117
Scientific journals
.................................................................................................................................. 121
The controversy of the infinite
.................................................................................................... 123
Dedekind
.....................................................................................:.............................................................. 124
Mittag-Leffler
........................................................................................................................................... 125
Cantor the eccentric
........................................................................................................................... 127
Mental illness
............................................................................................................................................ 128
Infinity in the 21st century
............................................................................................................. 129
Appendix
.................................................................................................................................................. 131
Bibliography
............................................................................................................................................ 135
Index
............................................................................................................................................................. 137
Into Infinity
Discovering a world without end
If the search for knowledge is compared to a treasure hunt, a
complete understanding of the theory of infinity would without
doubt be the greatest prize of all. Carving a path between dogma
and paradox, the concept of infinity has always been a nebulous
yet tangible presence in the landscapes of ancient philosophy,
medieval religion and modern science. This book follows the
elusive trail of infinity through the minds of philosophers,
theologians, physicists and, above all, mathematicians.
|
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| bvnumber | BV040697908 |
| classification_rvk | SN 100 |
| ctrlnum | (OCoLC)826610865 (DE-599)BVBBV040697908 |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T00:31:56Z |
| institution | BVB |
| language | English |
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| owner_facet | DE-703 |
| physical | 140 S. Ill., graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | RBA |
| record_format | marc |
| series2 | Everything is mathematical |
| spelling | Gracián, Enrique Verfasser aut Into infinity discovering a world without end Enrique Gracián London RBA 2013 140 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Everything is mathematical Unendlichkeit (DE-588)4136067-9 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Unendlichkeit (DE-588)4136067-9 s Mathematik (DE-588)4037944-9 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025678503&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025678503&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Gracián, Enrique Into infinity discovering a world without end Unendlichkeit (DE-588)4136067-9 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4136067-9 (DE-588)4037944-9 |
| title | Into infinity discovering a world without end |
| title_auth | Into infinity discovering a world without end |
| title_exact_search | Into infinity discovering a world without end |
| title_full | Into infinity discovering a world without end Enrique Gracián |
| title_fullStr | Into infinity discovering a world without end Enrique Gracián |
| title_full_unstemmed | Into infinity discovering a world without end Enrique Gracián |
| title_short | Into infinity |
| title_sort | into infinity discovering a world without end |
| title_sub | discovering a world without end |
| topic | Unendlichkeit (DE-588)4136067-9 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Unendlichkeit Mathematik |
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