The Continuum and Other Types of Serial Order

Edward V. Huntington

• Verlag: Dover Publications
• Jahr: 2017
• ISBN:
  9780486161075
• Thema: Matematica
• Thema: Matematica generale

"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.

Inhaltsverzeichnis

• Cover
• Title page
• Copyright
• Preface to the Second Edition
• Contents
• Introduction
• Chapter I On Classes In General
• Chapter II On Simply Ordered Classes, Or Series
• Chapter III Discrete Series: Especially The Type ω Of The Natural Numbers
• Chapter IV Dense Series: Especially The Type η Of The Rational Numbers
• Chapter V Continuous Series: Especially The Type θ Of The Real Numbers
• Chapter VI Continuous Series Of More Than One Dimension, With A Note On Multiply Ordered Classes
• Chapter VII Well-Ordered Series, With An Introduction To Cantor’S Transfinite Numbers
• Index Of Technical Terms