The Continuum, and Other Types of Serial Order: With an Introduction to Cantor's Transfinite Numbers (Classic Reprint) - Hardcover

Edward Vermilye Huntington

9780364316573: The Continuum, and Other Types of Serial Order: With an Introduction to Cantor's Transfinite Numbers (Classic Reprint)

Hardcover

ISBN 10: 0364316578 ISBN 13: 9780364316573

Publisher: Forgotten Books, 2018

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Explore how infinity is brought into clear, orderly form through Cantor’s ideas.

This accessible overview introduces the fundamentals of transfinite numbers, well‑ordered series, and the algebra of cardinal numbers. It offers a practical view of how continuous and discrete orders interact, and how foundational postulates shape the theory.

In this edition, you’ll see how the book builds from defining classes and their order to proving key properties of continuous series. It covers the concept of cardinal and ordinal numbers, how sums and products are defined for disjoint classes, and how operations on cardinals resemble familiar arithmetic. The material also touches on important questions about the continuum and the historical context of Cantor’s work.

Understand what a well‑ordered series is and why it matters for cardinal numbers
Learn how addition, multiplication, and exponentiation are defined for infinities
See examples that connect abstract postulates to concrete systems like the line or plane
Get a sense of the big questions, such as the size of the continuum, and the ideas behind their study

Ideal for readers of mathematical logic, set theory, and the foundations of mathematics who want a clear view of Cantor’s transfinite numbers and their consequences.

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