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 theoryuncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself. By focusing on the settheoretic aspects of analysis, this text makes the best of two worlds: it combines a downtoearth introduction to set theory with an exposition of the essence of analysisthe study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to "assume" the real numbers. Its prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the CantorSchroderBernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.
About John Stillwell
John Stillwell is a professor of mathematics at the University of San Francisco. He is also an accomplished author, having published several books with Springer, including Mathematics and Its History The Four Pillars of Geometry Elements of Algebra Numbers and Geometry and many more.Details Book
Author  :  John Stillwell 
Publisher  :  Springer International Publishing AG 
Data Published  :  16 October 2013 
ISBN  :  3319015761 
EAN  :  9783319015767 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  244 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
Reviews The Real Numbers

Margo Anderson Get eBook The Real Numbers
Finally I get this ebook, thanks for all these I can get now!

Lisa Doran Best website free download ebook
I was suspicious at first when i got redirected to the membership site. Now I'm really excited i found this online library....many thanks Kisses

Markus Jensen How to download The Real Numbers eBook?
I did not think that this would work, my best friend showed me this website, and it does! I get my most wanted eBook

Roddy Murray
My friends are so mad that they do not know how I have all the high quality ebook which they do not!

Lukasz Czaru
so many fake sites. this is the first one which worked! Many thanks


Andrew Smith
Just select your click then download link, and complete an offer to start downloading the ebook. If there is a survey it only takes 5 minutes, try any survey which works for you.

Kevin Mason
lol it did not even take me 5 minutes at all! XD

