Continuum and Other Types of Serial Order Book

	Introduction	1
Chapter I	On Classes in general
Section 1-6.	One-to-one correspondence between two classes	4
Section 7-10.	Finite and infinite classes	6
Section 11.	The simplest mathematical systems	8
Chapter II	On simply ordered Classes, or Series
Section 12-15.	Definition of a series: Postulates 1-3	10
Section 16.	Ordinal correspondence between two series	11
Section 17-18.	Properties of series. Successor. Predecessor	12
Section 19.	Examples of series	13
Section 20.	Examples of systems which are not series	16
Chapter III	Discrete Series: Especially the Type [omega] of the Natural Numbers
Section 21-22.	Definition of a discrete series: Postulates N1-N3	19
Section 23.	Theorem of mathematical induction	20
Section 24-27.	Properties of discrete series. Progressions, or series of type [omega]	21
Section 28.	Examples of discrete series; the natural numbers	23
Section 29.	Examples of series which are not discrete	23
Section 30-36.	On numbering the elements of a discrete series. Sums and products of the elements	25
Section 37-40.	On denumerable classes	30
Chapter IV	Dense Series: Especially the Type [eta] of the Rational Numbers
Section 41-43.	Definition of a denumerable dense series: Postulates H1-H2	34
Section 44-45.	Properties of denumerable dense series. Series of type [eta]	35
Section 46-50.	Segments. Limits	37
Section 51.	Examples of denumerable dense series; the rational numbers	39
Section 52.	Examples of series which are not dense	41
Section 53.	On the arithmetical operations among the elements of a dense series	43
Chapter V	Continuous Series: Especially the Type [theta] of the Real Numbers
Section 54-55.	Definition of a linear continuous series: Postulates C1-C3	44
Section 56-62.	Properties of linear continuous series. Series of type [theta]	45
Section 62a.	Digression on the theory of sets of points	52
Section 63.	Examples of linear continuous series; the real numbers	52
Section 64.	Examples of series which are not continuous	55
Section 65.	On the arithmetical operations among the elements of a continuous series	57
Chapter VI	Continuous Series of More than One Dimension, with a Note on Multiply Ordered Classes
Section 66-70.	Definition of n-dimensional continuous series. Series of type [theta superscript n]	58
Section 71.	The one-to-one correspondence between the points of all space and the points of a line	60
Section 72.	Note on multiply ordered classes	62
Chapter VII	Well-ordered Series, with an Introduction to Cantor's Transfinite Numbers
Section 73-76.	Definition of a well-ordered series: Postulates 4-6	63
Section 77-85.	Examples and properties of well-ordered series	66
Section 86.	The transfinite ordinal numbers; [omega], [Omega], etc.	73
Section 87-91.	The transfinite cardinal numbers; N[subscript 0], N[subscript 1], etc.	74
	Index of technical terms	81