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22 reviews(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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Product details:
ISBN 10: 0486495507
ISBN 13: 9780486495507
Author: Edward V Huntington
(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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Tags: Edward V Huntington, Continuum, Types, Serial Order