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(Ebook) Continuum and Other Types of Serial Order 2nd Edition by Edward V Huntington ISBN 9780486495507 0486495507

  • SKU: EBN-991852
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Authors:Edward V. Huntington
Pages:90 pages.
Year:2003
Editon:2
Publisher:Dover Publications
Language:english
File Size:6.59 MB
Format:pdf
ISBNS:9780486495507, 0486495507
Categories: Ebooks

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(Ebook) Continuum and Other Types of Serial Order 2nd Edition by Edward V Huntington ISBN 9780486495507 0486495507

(Ebook) Continuum and Other Types of Serial Order 2nd Edition by Edward V Huntington - Ebook PDF Instant Download/Delivery: 9780486495507 ,0486495507
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ISBN 10: 0486495507
ISBN 13: 9780486495507
Author: Edward V Huntington

"An admirable introduction to the rigorous theory of the continuum."—Science Progress "Extremely readable . . . a clear axiomatically constructed introduction."—Elemente der Mathematik This classic of mathematics presents the best systematic elementary account of the modern theory of the continuum as a type of serial order. Based on the Dedekind-Cantor ordinal theory, this text requires no knowledge of higher mathematics. Contents include a historical introduction and chapters on classes in general; simply ordered classes, or series; discrete series, especially the type of the natural numbers; dense series, especially the type of the rational numbers; continuous series, especially the type of the real numbers; continuous series of more than one dimension, with a note on multiply ordered classes; and well ordered series, with an introduction to Cantor's transfinite numbers. 1917 edition. 119 footnotes, mostly bibliographical.
 

(Ebook) Continuum and Other Types of Serial Order 2nd Edition Table of contents:

Chapter I On Classes In General

1–6. One-to-one correspondence between two classes

7–10. Finite and infinite classes

11. The simplest mathematical systems

Chapter II On Simply Ordered Classes, Or Series

12–15. Definition of a series: Postulates 1–3

16. Ordinal correspondence between two series

17–18. Properties of series. Successor. Predecessor

19. Examples of series

20. Examples of systems which are not series

Chapter III Discrete Series: Especially The Type ω Of The Natural Numbers

21–22. Definition of a discrete series: Postulates N1–N3

23. Theorem of mathematical induction

24–27. Properties of discrete series. Progressions, or series of type ω

28. Examples of discrete series; the natural numbers

29. Examples of series which are not discrete

30–36. On numbering the elements of a discrete series. Sums and products of the elements

37–40. On denumerable classes

Chapter IV Dense Series: Especially The Type η Of The Rational Numbers

41–43. Definition of a denumerable dense series: Postulates H1–H2

44–45. Properties of denumerable dense series. Series of type η

46–50. Segments. Limits

51. Examples of denumerable dense series; the rational numbers

52. Examples of series which are not dense

53. On the arithmetical operations among the elements of a dense series

Chapter V Continuous Series: Especially The Type θ Of The Real Numbers

54–55. Definition of a linear continuous series: Postulates C1–C3

56–62. Properties of linear continuous series. Series of type θ

62a. Digression on the theory of sets of points

63. Examples of linear continuous series; the real numbers

64. Examples of series which are not continuous

65. On the arithmetical operations among the elements of a continuous series

Chapter VI Continuous Series Of More Than One Dimension, With A Note On Multiply Ordered Classes

66–70. Definition of n-dimensional continuous series. Series of type θn

71. The one-to-one correspondence between the points of all space and the points of a line

72. Note on multiply ordered classes

Chapter VII Well-Ordered Series, With An Introduction To Cantor’S Transfinite Numbers

73–76. Definition of a well-ordered series: Postulates 4–6

77–85. Examples and properties of well-ordered series

86. The transfinite ordinal numbers; ω, Ω, etc

87–91. The transfinite cardinal numbers; N0, N1, etc

Index Of Technical Terms

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