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The real numbers : an introduction to set theory and analysis

Author: John Stillwell
Publisher: Cham [Switzerland] ; New York : Springer, [2013] ©2013
Series: Undergraduate texts in mathematics.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory"uncountability, the axiom of choice, and  Read more...
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Document Type: Book
All Authors / Contributors: John Stillwell
ISBN: 9783319015767 3319015761
OCLC Number: 856738499
Description: xvi, 244 pages : illustrations ; 25 cm.
Contents: The fundamental questions --
From discrete to continuous --
Infinite sets --
Functions and limits --
Open sets and continuity --
Ordinals --
The axiom of choice --
Borel sets --
Measure theory --
Reflections.
Series Title: Undergraduate texts in mathematics.
Responsibility: John Stillwell.

Abstract:

This text plugs a gap in the standard curriculum by linking set theory with analysis. It features a distinctive, detailed treatment of the real numbers system, and combines an introduction to set  Read more...

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"This is a book of both analysis and set theory, and the analysis begins at an elementary level with the necessary treatment of completeness of the reals. ... the analysis makes it valuable to the Read more...

 
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